Quantum Criticality and Topology in Correlated Electron Systems

We investigate from first-principles-derived models, possible momentum-dependent correlation effects, such as relative band shifts of electron and hole bands in opposite directions, by including non-local self-energy contributions within Random Phase Approximation (RPA). Comparison with results from Two-particle Self-Consistent (TPSC) approximation indicates that correlations in pnictide systems like LiFeAs can be described rather well by a non-local self-energy. In particular, the Fermi pocket shrinkage as seen in experiment occurs within the paradigm of interband scattering.

Motivated by recent experimental reports of significant spin-orbit coupling (SOC) and a sign-changing order-parameter in the Li$_{1-x}$Fe$_x$(OHFe)$_{1-y}$Zn$_y$Se superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states - $s$-wave, $d$-wave and helical $p$-wave - can have a fully gapped density of states (DOS) consistent with angle-resolved photoemission spectroscopy (ARPES) experiments and, due to spin-orbit coupling, are a mixture of spin singlet and triplet components leading to intra- and inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spin-triplet dominated even parity $A_{1g}$ (s-wave) and $B_{2g}$ (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments.

The parton construction is a useful construction to study frustrated magnets in 2+1 dimensions. The Dirac spin liquid (DSL) is a description of such materials when fermionic partons are used and the mean-field ansatz has Dirac cones in its spectrum. At low energies, the DSL is described by compact Quantum Electrodynamics in 2+1D ($QED_3$) with $N_f$ fermions, i.e. a $U(1)$ gauge field coupled to $N_f$ relativistic fermions and with allowed monopole configurations. Monopoles are essential to determine if the DSL is a stable phase of matter or between which phases it could describe a phase transition. Previous works have focused on the $N_f=4$ case, as this is the most common case because generically in 2D there will be an even number of Dirac cones and there is also to possible spins. In this work, we study the case with $Nf=2n \geq 4 $ inspired by previous studies of Spin-Orbital quantum liquids [1] ($N_f=8$) as well as to make some progress to understand compact $QED_3$. This work is in collaboration with Chong Wang and is a follow-up to arxiv:1811.11182 and arxiv:1811.11186. [1] https://link.aps.org/doi/10.1103/PhysRevX.2.041013.

Interacting Dirac fermions exhibit perhaps the simplest example of fermionic quantum criticality. In high energy physics this has been known for some time, and goes under the guise of spontaneous fermion mass generation and chiral symmetry breaking in the Gross- Neveu-Yukawa model. The prototypical condensed matter example is the class of semimetal-insulator transitions on the half-filled honeycomb lattice, which are driven by on- site and nearest-neighbour repulsive interactions. The low energy excitations are well described by Dirac fermions, which couple to the dynamical order-parameter mass fields and play a crucial role in determining the universal behaviour. Naturally, this variety of criticality is outside of the Ginzburg-Landau-Wilson paradigm. We extend this idea by considering the situation where repulsive interactions induce charge order that spontaneously breaks translational and other crystal symmetries, which would clearly be forbidden in the high energy context. Unsurprisingly, the resulting effective field theory contains Lorentz-violating order parameter fields that couple to the Dirac fermions as emergent gauge fields. We analyse the criticality arising from the non-trivial interplay of mass and gauge fields with the renormalization group. In addition, topological phase transitions are natural to describe with this interplay.

Spatial modulations are argued to play an important rule in the mystery of high-temperature superconductors. By now, many studies have shown evidence for such an order, interpreting it mainly as charge or pairing density wave (CDW/PDW). We model the X-ray scattering experiments using a density-density response function of a fermionic model with minimal nearest and next-nearest neighbor hopping. By taking into account a pairing channel along the charge one, we show that this model is sufficient to account for the experimental data, and is giving a way to distinguish between the different modulations. In the light of the latest experiments, our model favors the PDW scenario as an explanation to the observed phenomena. In addition, a complementary self-consistent calculation is performed via the Hubbard model, enable us to assess which of the two contributions is more dominant in each case.

Motivated by the long standing experimental mystery of the observation of a melting transition seemingly in the 3-state Potts universality class in thin films of liquid crystals, we revisit a model of coupled XY models. In these compounds, the interplay of the hexatic and nematic degrees of freedom, respectively invariant under rotation by $\pi$ and by $\pi/3$, leads to emergent discrete variables through the resulting anisotropic coupling. Using both large scale Monte-Carlo algorithms, with an adapted Wolff step and parallel tempering, and analytical methods, such as real-space renormalization group, we study the phase diagram of such a coupled XY model with global $U(1) \times \mathbb{Z}_3$ symmetry. The presence of the discrete order can highly frustrate the possible binding of vortices, and we investigate how this non-trivial interaction can lead to unconventional arrangements of the vortices. Our extensive numerical study focuses on the regime where both XY-type hexatic and nematic variables are equally present, and we discuss the possibility of a 3-state Potts transition at higher temperature than the BKT transition, as well as the nature of the meeting point between the BKT and Potts phase transition. We acknowledge financial support by the DOE, Basic Energy Sciences grant DE-FG02-99ER45790, and the Quebec FRQNT.

Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. In this work we show that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e. power-law) solutions, corresponding to the metastable insulator at the boundary of metal-insulator coexistence region, which can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a \emph{different} power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and hence responsible for the apparent quantum critical scaling above the classical critical end point.

Recently discovered [1] superconductivity (SC) in twisted bilayer graphene (TBG) shares several qualitative features with that observed in high-$T_c$ cooper oxides. Yet, the relation between the pairing mechanism in these classes of materials remains unclear with both local-correlation and phonon-driven scenarios proposed for TBG. In the first part of the talk I will report on our variational statistically-consistent Guztwiller (SGA) study of the tiangular-lattice, two-orbital Hubbard model of moir\'{e} superlattice with approximate $SU(4)$ symmetry, based on the early effective Hamiltonian of Xu and Balents [2]. The calculated phase diagram [3] encompasses two asymmetric SC domes around the Mott-insulating state near half-filling. Remarkably, we obtain a broad SC$+$Mott insulator \textit{phase separation regime}, which is consistent with phase-coherent transport observed experimentally in applied magnetic field [1]. Within the present approach, SC turns out to be of topological spin-triplet, orbital-singlet $d_{x^2-y^2}+id_{xy}$ character and is driven primarily by combined effect of strong on-site Coulomb repulsion and magnetic exchange. The \textit{topological edge states} are identified by the analysis of electronic spectral function for the system with cylindrical geometry. In the second part, I will briefly comment on certain formal analogies between the discussed pairing mechanism for TBG and that relevant to the class of ferromagnetic superconductors $\mathrm{UGe_2}$, $\mathrm{URhGe}$, $\mathrm{UCoGe}$, and $\mathrm{UIr}$ [4]. Our extended four-orbital Anderson-lattice model of $\mathrm{UGe_2}$, with the $f$-electron sector interaction structure very similar to that employed for the two-orbital model of the TBG, qualitatively reproduces the experimental series of the first-order SC and metamagnetic phase transitions in the pressure-magnetic field plane [5]. This work was supported by the Grant OPUS No. UMO-2018/29/B/ST3/02646 from Narodowe Centrum Nauki (NCN). \vspace{1em} [1] Y. Cao \textit{et al}., Nature \textbf{556}, 43 (2018); \textit{ibid}. \textbf{556}, 80 (2018). [2] C. Xu and L. Balents, Phys. Rev. Lett. \textbf{121}, 087001 (2018). [3] M. Fidrysiak, M. Zegrodnik, and J. Spa{\l}ek, Phys. Rev. B \textbf{98}, 085436 (2018). [4] D. Aoki, K. Ishida, and J. Flouquet, J. Phys. Soc. Japan \textbf{88}, 022001 (2019). [5] E. K\k{a}dzielawa-Major, M. Fidrysiak, P. Kubiczek, and J. Spa{\l}ek, Phys. Rev. B \textbf{97}, 224519 (2018); M. Fidrysiak, D. Goc-Jag{\l}o, E. K\k{a}dzielawa-Major, P. Kubiczek, J. Spa{\l}ek, \textit{ibid.} 2019 (accepted).

1T-TaS$_2$ is an archetypal layered compound where Mott insulator coexists with charge-density wave. Its insulating state can be suppressed in favor of metallic and superconducting ones with multiple parameters like pressure, chemical doping or substitution. More intriguingly, it was recently realized that the new long-living metastable domain-like metallic state can be created out of equilibrium with a single ultrashort optical [1] or electrical pulse [2], giving access to exploring the non-equilibrium states with “slow” techniques. Here we combine multi-probe scanning tunneling microscopy and spectroscopy with an in situ ultrafast optical excitation to explore the non-equilibrium phase diagram of 1T-TaS$_2$ [3, 4] and identify non-equilibrium ordering mechanisms and the origin of metastability. In the domain-like state we observe the phase locking between different domains, which gives the nice evidence of an existence of a long-range ordering at non-equilibrium conditions. The long-term metastability emerges via interplay between long-range ordering and formation of charge density wave dislocations [3]. Far more unexpected outcome is the formation of a metastable amorphous state where part of the electrons is localized into an amorphous hyperuniform pattern on the triangular atomic lattice, which retains its perfect order [4]. The mechanism for its formation can be attributed to a dynamical localization of electrons through mutual interactions akin to jamming, whereas a metastability stems from the overconstrained motion of individual particles. We will also discuss the emergence of metallic or variable-range hopping transport which occurs on top of the Mottness collapse in these states. This work was supported by the ERC Advanced Grant »Trajectory« and ARRS P1-0040. [1] L. Stojchevska et al., Science 344, 177 (2014) [2] L. Ma et al., Nat. Comm. 7, 10956 (2016); D. Cho et al., Nat. Comm. 7, 10453 (2016), I. Vaskivskyi et al., Nat. Comm. 7, 11442 (2016). [3] Ya. Gerasimenko et al., arXiv:1704.08149v2 (2017) [4] Ya. Gerasimenko et al., arXiv:1803.00255 (2018) (accepted to Nat. Mater., 2019)

We propose a single-site mean-field description, suitable for narrow-band systems with interaction-induced hybridisation at finite temperatures. Presently this approach, based on the notion of a fluctuating on-site density matrix (OSDM), is developed for the case of extended Falicov-Kimball model (EFKM). In an EFKM, an excitonic insulator phase can be stabilised at zero temperature. With increasing temperature, the excitonic order parameter (interaction-induced hybridisation on-site, characterised by the absolute value and phase) eventually becomes disordered, which involves fluctuations of both its phase and (at higher T) its absolute value. In order to build an adequate finite-temperature description, it is important to clarify the nature of degrees of freedom associated with the phase and absolute value of the induced hybridisation, and correctly account for the corresponding phase space volume. We show that the OSDM-based treatment of the local fluctuations indeed provides an intuitive and concise description (including the phase space integration measure). This allows to describe both the lower-temperature regime where phase fluctuations destroy the long-range order, and the higher temperature crossover corresponding to a decrease of absolute value of the hybridisation relative to the fluctuations level. This picture is also expected to be relevant in other contexts, including the Kondo lattice model.

TBA

We provide a detailed analysis of a realization of chiral gapless edge modes in the framework of the Hofstadter model of interacting electrons. In a transverse homogeneous magnetic field and a rational magnetic flux through an unit cell the fermion spectrum splits into topological subbands with well-defined Chern numbers, contains gapless edge modes in the gaps. It is shown that the behavior of gapless edge modes is described within the framework of the Kitaev chain where the tunneling of Majorana fermions is determined by effective hopping of Majorana fermions between chains. The proposed approach makes it possible to study the fermion spectrum in the case of an irrational flux, to calculate the Hall conductance of subbands that form a fine structure of the spectrum. In the case of a rational flux and a strong on-site Hubbard interaction $U$, $ U >4 \Delta $ ($ \Delta $ is a gap), the topological state of the system, which is determined by the corresponding Chern number and chiral gapless edge modes, collapses. When the magnitude of the on-site Hubbard interaction changes, at the point $ U = 4 \Delta $ a topological phase transition is realized, i.e., there are changes in the Chern numbers of two subbands due to their degeneration.

Phase transformations induced by ultra-short optical pulses present a mainstream in studies of cooperative electronic states. In a system prone to a thermodynamic instability, a dynamical phase transition can be provoked by optical pumping to excitons. We present a semi-phenomenological modelling of spacio-temporal effects expected when the density of optical excitons is linearly coupled with the order parameter as it happens in organic donor-acceptor compounds with neutral-ionic ferroelectric phase transitions. To describe both thermodynamic and dynamical effects on equal footing, we adopt for the phase transition a view of the “excitonic insulator” state and suggest a formation of the macroscopic quantum state for the pumped excitons. The double nature of the ensemble of excitons leads to an intricate time evolution: the dynamical transition between number–preserved and phase–locked regimes, macroscopic quantum oscillations from interference between the Bose condensate of excitons and the ground state of the excitonic insulator. Modeling of an extended sample shows also stratification in domains of low and high densities which evolve through local dynamical phase transitions and a sequence of domains’ merging.

In the present work we consider the excitonic effects in the twisted bilayer graphene within the rotated bilayer Hubbard model. Both, intralayer and interlayer Coulomb interaction have been considered and the half-filling condition is imposed for the electronic densities is both layers of the bilayer graphene system. We calculate the excitonic pairing gap parameter and the chemical potential for different twisting angles and different values of the interlayer Coulomb interaction parameter. Furthermore, we show the appearance of the electronic flat bands in the electronic band structure of the system, for different twist angles.

Topological Kondo insulators (TKIs) are a special class of topological insulators, emerging through the interplay of strong correlations and spin-orbit coupling. In TKIs, the bulk is a narrow-band insulator due to the appearance of a localized Kondo resonance near the Fermi level and its hybridization with the conduction band. Additionally, the strong spin-orbit coupling of the localized moments generates a non-local hybridization between the local moments and the conduction band, which results in a topologically nontrivial band structure and gapless surface states. In the past, TKIs have been described predominantly by slave-boson mean-field (SBMF) calculations. Such static methods are unable to capture finite-lifetime effects of the heavy Kondo quasiparticles, which become important when the topological gap closes at the surface of a TKI. We design a spin-orbit coupled dynamical mean-field theory with an auxiliary-particle conserving approximation as the impurity solver. With this, we aim at calculating characteristic, observable quantities, like the surface conductivity, and thus the fate of a topologically stabilized surface state.

Abstract: Using exact quantum Monte Carlo method, we identify the phase diagram of the half filled, the lightly doped and heavily doped graphene, which shows a rather rich physical properties. At half filling, the system is driven to a Mott insulator with antiferromagnetic long range order by increasing interaction, and a transition from a d+id pairing to a p+ip pairing is revealed, depends on the next-nearest hoping and the electronic fillings. We also examine the recent novel electronic states seen in magic-angle graphene superlattices. From the Hubbard model on a double-layer honeycomb lattice with a rotation angle $\theta$=1.08, we reveal that an antiferromagnetically ordered Mott insulator emerges beyond a critical U c at half filling, and with a small doping, the pairing with d+id symmetry dominates over other pairings at low temperature. The effective d+id pairing interaction strongly increase as the on-site Coulomb interaction increases, indicating that the superconductivity is driven by electron-electron correlation. Our non-biased numerical results demonstrate that the twisted bilayer graphene share the similar superconducting mechanism of high temperature superconductors, which is a new and idea platform for further investigating the strongly correlated phenomena. References: Ma, Huang, Hu, and Lin, Phys. Rev. B 84, 121410(R) (2011). Ma, Yang, Yao, and Lin, Phys. Rev. B 90, 245114 (2014). Ma, Zhang, Chang, Huang and Richard, Phys. Rev. Lett. 120,116601 (2018). Huang, Zhang and Ma*, Science Bulletin 64,310(2019). Chen, Chu, Huang and Ma*, arXiv:1903.01701(2019).

We find that heavy fermion systems can have bulk "Fermi arcs'', with the use of the non-Hermitian topological theory. In an interacting electron system, we can define the effective Hamiltonian $H_{\rm eff} = H + \Sigma$ , where the microscopic many-body Hamiltonian is Hermitian, but the one-body quasiparticle Hamiltonian is non-Hermitian due to the finite quasiparticle lifetime. A possible mechanism of a Fermi arc has proposed in a Dirac material in two dimensions[1,2]. By introducing a topological theory of finite-lifetime quasiparticles, we can find that the low-energy dispersion of the Dirac material is reshaped and a topologically protected bulk Fermi arc appears. Finite quasiparticle lifetime is a generic property of quantum many body systems, resulting from either inelastic electron-electron/electron-phonon scattering at finite temperatures, or elastic electron-impurity scattering. The exceptional points of the non-Hermitian quasiparticle Hamiltonian matrix play a crucial role. With the use of the dynamical mean field theory (DMFT) calculation, we confirm our statement in Kondo insulators with a momentum-dependent hybridization in two-dimensions. We show that the concept of the exceptional points in the non-Hermitian quasiparticle Hamiltonian is one of powerful tools to predict new phenomena in strongly correlated electron systems[3]. [1]H. Shen, B. Zhen, and L. Fu, Phys. Rev. Lett. 120, 146402 (2018). [2]V. Kozii and L. Fu, arXiv:1708.05841 [3] Y. Nagai, Yang Qi, Hiroki Isobe, Vladyslav Kozii, and Liang Fu, in preparation.

Many transitional metal oxides demonstrate complicated phase diagrams [1]. Molybdenum oxides in particular exhibit charge density wave (CDW) and superconductive phases upon alkali doping [2] or oxygen reduction to stoichiometric Mo$_n$O$_{3n-1}$ family, but rarely demonstrate the strongly-correlated behavior. The semi-metallic Mo$_8$O$_{23}$ crystals from the latter family are different – in addition to the room-temperature CDW [3] they demonstrate another lower temperature ordering not related to any structural transformation, as was suggested by the observation of the multicomponent transient reflectivity [4] and non-monotonic transport response [3]. This is further supported with the scanning tunneling spectroscopy studies that reveal gradual gap opening at the CDW transition and another rapid increase in the gap value below ~30 K, that we associate with the new correlated non-magnetic order competing with the CDW [5]. Surprisingly an exposure to a single ultrashort threshold optical pulse changes the temperature dependence of the gap, stabilizing the low-temperature correlated order at the temperatures all the way up to CDW transition without any effect on the crystal topography. Spatially-resolved tunneling spectroscopy reveals the charge inhomogeneity in the low-temperature phases of both pristine and exposed areas with a tendency to stripe-like order. These results demonstrate the possibility of the optical control of the electronic rather than structural ordering in the correlated oxides. [1] E. Dagotto, Science 309, 257–262 (2005). [2] J.-P. Pouget, Low-Dimensional Electronic Properties of Molybdenum Bronzes and Oxides (ed. C. Schlenker) (KluwerAcademic Press, Dordrecht, 1989). [3] M. Sato, H. Fujishita, S. Sato, and S. Hoshino, J. Phys. C: Solid State Phys. 19, 3059 (1986). [4] V. Nasretdinova et.al, Phys. Rev. B 99, 085101 (2019). [5] V. Nasretdinova et.al, under review in Scientific reports.

Due to fascinating phenomena such as magneto-electronic phase separation and Co ion spin-state transitions, the archetypal cobaltite La$_{1-x}Sr$_x$CoO$_{3-\delta}$ (LSCO) remains of high interest. Chemical substitution of La by Sr introduces both holes and magnetic moments into the diamagnetic parent compound. The tendency of Co to undergo spinstate transitions leads to the formation of 7-site spin polarons. Further doping results in a glassy magnetic state that transforms at x=0.18 into a ferromagnetic metal. As simple statistical considerations predict a percolation of polarons at much smaller values of x=0.05, this raises the question what suppresses the formation of ferromagnetism. Here, we address this question within a microscopic model capturing both competing magnetic interactions between the Co moments in different spin states as well the spatial inhomogeneity introduced by disorder. Large-scale parallel tempering classical Monte-Carlo simulations reveal that the origin of the delayed percolation transition lies in the frustration of ferromagnetic polarons via competing (anti-)ferromagnetic interactions. Our simulations explicitly show how frustrated polarons act as seeds of the observed magneto-electronic phase separated glassy state at intermediate doping 0.05 < x < 0.18, providing a consistent microscopic understanding across the full doping range.

We revisit the problem of two dimensional metals in the vicinity of a quantum phase transition to incommensurate Q=2kF charge density wave order, where the order parameter wave vector Q connects two hot spots on the Fermi surface with parallel tangents. Earlier theoretical works argued that such critical points are potentially unstable, if the Fermi surface at the hot spots is not sufficiently flat. Here we perform a controlled, perturbative renormalization group analysis and find a stable fixed point corresponding to a continuous quantum phase transition, which exhibits a strong dynamical nesting of the Fermi surface at the hot spots. We derive scaling forms of correlation functions at the critical point and discuss potential implications for experiments with transition metal dichalcogenides and rare-earth tellurides.

We study magnetic quantum oscillations in two very different materials: organic antiferromagnetic conductor $\kappa$-(BETS)$_2$FeBr$_4$ and electron-doped cuprate superconductor Nd$_{2−x}$Ce$_x$CuO$_4$. We focus on spin modulation of the Shubnikov–de Haas (SdH) oscillations, a sensitive technique to quantify the Zeeman effect. In both materials, the quantum oscillation amplitude showed no spin-zeros in the entire range of tilt angles $0< \theta \lesssim 70^{\circ}$ where we observed the oscillations, consistently with the physics of the Zeeman spin-orbit coupling in antiferromagnetic conductors.[1-5] 1. R. Ramazashvili, Phys. Rev. Lett. 101, 137202 (2008). 2. R. Ramazashvili, Phys. Rev. B 79, 184432 (2009). 3. R. Ramazashvili, Phys. Rev. B 80, 054405 (2009). 4. V.V. Kabanov and A. S. Alexandrov, Phys. Rev. B 77, 132403 (2008); 81, 099907(E) (2010). 5. R. Ramazashvili, Phys. Rev. Lett. 105, 216404 (2010).

Twisted bilayer graphene has recently attracted a lot of attention for its rich electronic properties and tunability. In particular, the discovery of Mott insulating regime and superconductivity in magic angle graphene superlattices ($\alpha \approx 1^\circ$) highlights the potential to realize tunable flat bands and strong correlations in pure graphene platforms. Here we show that for very small angles, $\alpha \ll 1^\circ$, the application of a perpendicular electric field is mathematically equivalent to a gauge field. This mapping allows us to predict the emergence of highly localized modes that are associated with flat bands close to charge neutrality, and whose energy can be tuned by the electric interlayer bias. Interestingly, the electrically generated localized modes closest to charge neutrality form an emergent Kagome lattice, in contrast to the triangular lattice formed by the flat bands at the magic angles. Our findings indicate that for tiny angles, biased twisted bilayer graphene is a promising platform which can realize frustrated lattices of highly localized states, opening a new direction for the investigation of strongly correlated phases of matter.

At low temperatures, isotropic two-dimensional Fermi systems with quadratic band touching (QBT) are unstable with respect to a symmetry-broken ground state, once interactions are taken into account. Bernal-stacked honeycomb bilayers (such as bilayer graphene) are host to QBTs under suitable assumptions, but their rotational symmetry is only threefold ($C_3$). Although the symmetry-breaking terms present in the tree-level Hamiltonian are power-counting irrelevant, they lead to a dynamical splitting of the QBT into Dirac cones under renormalization group (RG) flow. This we demonstrate by explicitly evaluating the nontrivial two-loop self-energy correction (the one-loop contribution vanishes for local 4-Fermi interactions). We thus derive improved RG flow equations, allowing us to map out the quantum phase diagramme. We show that the dynamically generated Dirac cones stave off spontaneous symmetry breaking at infinitesimal interaction strengths, giving way to a transition only at finite coupling. The latter is governed by a quantum critical point of the Gross-Neveu universality class, with emergent Lorentz symmetry. We also work out consequences of our RG flow for finite temperature physics, in particular a crossover between dynamical critical exponent $z = 2$ at intermediate $T$ and $z = 1$ at low $T$.

The conventional theory of optical responses in metals has been based on the Drude theory, which relies on the assumption that electron-electron scattering is weak enough to ignore and the transport is governed by collisions with defects or phonons. In recent years, however, it has become possible to prepare ultrapure metallic samples, such as PdCoO2 [1], graphene [2], and GaAs/AlGaAs heterostructures [3], where the electron-electron scattering becomes most dominant process governing transport and thus the Drude theory is no longer valid. This regime is called “hydrodynamic regime” and described by an emergent hydrodynamic theory. In fact, many pieces of evidence of hydrodynamic effects in DC transport have already been reported. In our work, we develop a basic framework of optical response in the hydrodynamic regime. Based on the Navier-Stokes equation, we compute the reflectance and the transmittance in three-dimensional (3D) electron fluids. We find that, in the hydrodynamic regime, there are two propagating mode with different dispersion relations. Our formulation describes how to optically probe the hydrodynamic effects, enabling us to measure the viscosity of 3D electron fluids by simple optical techniques. [1] Philip J. W. Moll, et al, Science 351 (2016) 1061. [2] D. Bandurin, et al, Science 351 (2016) 1055. [3] L. W. Molenkamp and M. J. M. de Jong, Phys. Rev. B 49 (1994) 5038.

We consider a strongly spin-orbit coupled metal, one of whose Fermi surfaces is close to a Lifshitz (topological) transition. Via a renormalisation group analysis of the square-lattice Hubbard model with strong Rashba spin-orbit coupling, we show that such a metal is generically unstable to the formation of mixed-parity superconductivity with a helical triplet component.

Recent studies show that ferroelectric materials can be tuned to second-order quantum criticality. Doping these systems gives rise to quantum critical polar metals, where structural phase transitions formally replace ferroelectric ones. This raises the following key questions: how does the presence of itinerant carriers alter the nature of the transition and what is the interaction between the electrons in the novel quantum critical fluid? Motivated by these considerations we study models of polar metal systems and investigate the possible coupling mechanisms of the conduction electrons to the critical mode. We find that the coupling is most effective in systems with multiple conduction bands crossing the Fermi energy simultaneously. In particular, the interaction effects should be pronounced near the points or lines where the bands cross. We further develop a description of such band crossings near polar metal quantum criticality. Experimental implications for doped strontium titanate and similar systems are discussed.

We propose a lattice scale two-band generalized Hubbard model as a caricature of the electronic structure of twisted bilayer graphene. Various possible broken symmetry phases can arise, including a nematic phase (which is a form of orbital ferromagnet) and an orbital-triplet spin-singlet superconducting phase. Concerning the mechanism of superconductivity -- we propose an analogy with superconductivity in alkali-doped $C_{60}$ in which a violation of Hund's first rule plays a central role. This abstract is subject to update based on on-going work in progress.

The Kitaev honeycomb magnet realizes an Abelian spin liquid ground state that can be driven to a non-Abelian spin liquid upon breaking time-reversal symmetry, e.g., by applying a magnetic field. Using Raman spectroscopy we show that in the candidate material $\alpha$-RuCl$_3$ a Majorana bound state emerges in the vicinity to quantum criticality out of a gapped continuum of deconfined Majorana fermions. We comment on the role of non-Kitaev terms in $\alpha$-RuCl$_3$ and determine the binding energy through a detailed temperature- and field-dependent study. Work supported by QUANOMET NL-4 and DFG LE967/16-1.

Recent experiments with ultra-cold atoms in an optical lattice have realized cavity-mediated global range and observed the emergence of a supersolid and a density wave phase in addition to Mott insulator and superfluid phases. Here we consider theoretically the effect of uncorrelated disorder on the phase diagram of this system and study the two-dimensional Bose-Hubbard model with global range interactions and uncorrelated diagonal disorder. With the help of quantum Monte Carlo simulations using the Worm algorithm, we determine the phase diagram of this model. We show that two kinds of Bose glass phases exist: one with and one without density wave order and discuss the nature of the various phase transitions that occur.