Constrained Many-body Dynamics

We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a charge-density wave state would show results similar to those of Schreiber {\it et al.\/} [{\it Science\/} {\bf 349}, 842 (2015)].

We analyze a different single-particle localization mechanism as a starting point for typical Many-Body Localization (MBL) studies. Rather than disorder we consider particles in the presence of a linear potential, which in the non-interacting limit exhibit well-known Wannier-Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient, these models exhibit behavior very similar to that obtained for disorder as indicated by their spectral and dynamical properties. These models, therefore, may constitute a new class of generic non-random models that fail to thermalize. They suggest new directions for experimentally exploring and understanding the phenomenon of MBL. If time permits, I wish to shortly mention a machine learning based consideration of finite size scaling for the MBL problem.

We study the low temperature static and dynamical properties of the classical bond-disordered antiferromagnetic Heisenberg model on the kagome lattice. Its groundstates can be understood to satisfy a set of local constraints exactly matching the number of degrees of freedom. We find {\it discrete} degenerate ground states in presence of arbitrary (bounded) disorder whose number grows exponentially with system size. These states do not exhibit zero-energy `excitations' characteristic of highly frustrated magnets but instead are local minima of the energy landscape, albeit with an anomalously soft excitation spectrum. This represents a spin liquid version of the phenomenon of jamming familiar from granular media and structural glasses. Correlations of this jammed spin liquid, which upon increasing the disorder strength gives way to a conventional spin glass, may be algebraic (Coulomb-type) or exponential. Surprisingly, despite the rigidity of the groundstates, we establish the vanishing of the corresponding spin stiffness. The spin dynamics resembles that of Coulomb Heisenberg spin liquids, but exhibits a new low-temperature dynamically arrested regime, which however gets squeezed out with increasing system size, in correspondence with a detailed study of the energy landscape which exhibits vanishing energy barriers between ground states and appears highly connected.

I will describe some of our recent efforts in understanding the excitation dynamics of quantum spin ice, a model system for studying three dimensional U(1) quantum spin liquid. In the first part of the talk, I will present a partial solution to a toy model that captures the essential features of single spinon, or "magnetic monopole", dynamics in quantum spin ice. I will demonstrate that the highly-constrained motion of spinon can be mapped to a random walk with entropy-induced memory. Direct simulation of this random walk shows that the spinon can nevertheless propagate coherently at long distances despite the constraint. In the second part of the talk, I will present our numerical simulation of a quantum spin ice model, where we observe and characterize the signatures of emergent photons and spinons in the dynamic spin structure factor through a combination of QMC simulation and stochastic analytic continuation.

We consider the quench dynamics of a two-dimensional (2D) constrained quantum dimer model and determine its rich dynamical phase diagram. By means of exact diagonalization on systems of sizes up to 8x8 we show that properly defined order parameters relax to their thermal expectation values. This allows us to study the underlying equilibrium phase transitions in a dynamical context: a BKT-transition between a columnar ordered valence bond solid (VBS) and a valence bond liquid (VBL), as well as a first order transition between a staggered VBS and the VBL. For quenches across the BKT transition, the Loschmidt rate develops conventional non-analyticities at the zero-crossings of the order parameter, fixed by microscopic parameters. By contrast, the relaxation time across the first order transition scales linearly with the correlation length of the initial state, preventing the formation of sharp kinks. Within the staggered VBS, some local observables even fail to thermalize as a result of the kinematic constraints of the quantum dimer model.

The statistical mechanics description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. For quantum many-body systems statistical mechanics predicts the equilibration of highly excited non-equilibrium state towards a featureless thermal state. Hence, it is highly desirable to explore possible ways to avoid ergodicity in quantum systems. Many-body localization presents one generic mechanism for a strong violation of ergodicity relying on the presence of quenched disorder. In my talk I will discuss a different mechanism of the weak ergodicity breaking relevant for the experimentally realized Rydberg-atom quantum simulator [1]. This mechanism arises from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems [2]. In the single-particle case, quantum scars correspond to wave functions concentrated in the vicinity of unstable periodic classical trajectories. I will demonstrate that many-body scars appear in the Fibonacci chain, a model with a constrained local Hilbert space which can be realized by a Rydberg chain. The quantum scarred eigenstates are embedded throughout the otherwise thermalizing many-body spectrum but lead to direct experimental signatures, as I show for periodic recurrences that reproduce those observed in the experiment [1]. Finally, I will construct the weak deformation of the Rydberg chain Hamiltonian that makes revivals virtually perfect [3]. I will conclude with discussing a new opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable and possible generalizations of these results. \\ [1] Bernien, H. et al., Nature 551, 579–584 (2017), arXiv:1707.04344 \\ [2] C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, Z. Papić, Nature Physics (May 2018), arXiv:1711.03528 and Phys. Rev. B 98, 155134 (2018) arXiv:1806.10933 \\ [3] S. Choi, C. J. Turner, et al. arXiv:1812.05561

Fractons are a special type of emergent particle which obey not only conservation of charge, but also of higher charge moments, such as the dipole moment. In this talk, based on work in collaboration with Shriya Pai and Rahul Nandkishore, I will describe how the conservation of dipole moment leads to severe restrictions on the dynamics of fractons and can prevent the system from reaching thermal equilibrium. Specifically, we study one-dimensional fracton systems evolving under random unitary dynamics, subject only to the conservation of charge and dipole moment. We show that, when initialized with a single charge, the system forever remembers the initial position of the fracton, failing to reach thermal equilibrium. When the system is initialized with multiple fractons, all charges agglomerate to form a single density peak at their collective center of mass. We also study one-dimensional fracton systems undergoing periodic time evolution. In such Floquet systems, we can study the eigenstates of the time evolution operator and their entanglement spectra. We find that a Floquet fracton system hosts a small number of non-thermalizing eigenstates, obeying semi-Poisson statistics in their entanglement spectra, while the majority of the spectrum is thermal, obeying Wigner-Dyson statistics. We argue that the non-thermalizing states provide an example of quantum many-body scars.

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body ``scar states'' showing nonthermal behavior in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at \emph{infinite temperature} that can be represented exactly as matrix product states with \emph{finite} bond dimension, for both periodic boundary conditions (two exact $E = 0$ states) and open boundary conditions (two $E = 0$ states and one each $E = \pm \sqrt{2}$). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model and uncovers exact quantum many-body scar states. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in 1d at infinite temperature. We show that the nearby many-body scar states can be well approximated as ``quasiparticle excitations" on top of our exact $E = 0$ scar states, and propose a quasiparticle explanation of the strong oscillations observed in experiments.

Among the original magnetic states which emerge from frustrated magnetic systems, spin ice has aroused a strong interest because beyond its macroscopically degenerate ground state, the excitations can be described as magnetic charges, called magnetic monopoles. At very low temperature, below 200 mK, spin ice dynamics is governed by these monopoles. By performing thermal quenches in spin ice compounds down to these temperatures, through a specific protocol called "avalanche quench" [1], we are able to prepare samples with a very large out-of-equilibrium density of metastable magnetic monopoles. We used this method to study the monopole dynamics in the spin ice compounds Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$, and could measure the monopole current as a function of magnetic field [2]. In this talk, I will present some of our recent results which show that even below 200 mK, there is a fast recombination of magnetic monopoles. The comparison between magnetic relaxation measurements performed on several samples with different isotopes gives insights on the quantum tunneling mechanism governing the hopping of monopoles on the lattice, and shows the role of the dynamic coupling between the hyperfine fields and the electronic spins associated with magnetic monopoles. [1] C. Paulsen et al., Nature Physics 10, 135 (2014) [2] C. Paulsen et al., Nature Physics 12, 661 (2016)

Fractionalized Fermi liquids (FL*) have been introduced as non-Fermi-liquid metallic phases, characterized by coexisting electron-like charge carriers and local moments which itself form a fractionalized spin liquid. Here we investigate a Kondo lattice model on the honeycomb lattice with compass interactions among the local moments, a concrete model hosting FL* phases based on Kitaev's Z2 spin liquid. We characterize the FL* phases via perturbation theory, and we employ a Majorana-fermion mean-field theory to map out the full phase diagram. Most remarkably we find nematic triplet superconducting phases which mask the quantum phase transition between fractionalized and conventional Fermi liquid phases. Their pairing structure is inherited from the Kitaev spin liquid, i.e., superconductivity is driven by Majorana glue.

Rydberg lattice gases provide a versatile platform for studies of quantum few-body and many-body phenomena with applications ranging from quantum information processing to simulations of complex condensed matter systems. Of particular interest is the so-called facilitation mechanism (or anti-blockade), where the excitation of an atom to a Rydberg state is strongly enhanced in the vicinity of an already excited atom. This effect is of broad relevance and exploited in the design of quantum gates as well as in protocols for dissipative quantum state preparation. In the many-body context it effectuates an aggregation mechanism, where an initial Rydberg excitation seed triggers a dynamical growth of excitation clusters, and it enables the implementation of kinetic constraints thereby connecting to the physics of glass-forming substances. I will focus in my talk on the dynamics of Rydberg excitations in an optical tweezer array under facilitation conditions [1]. Due to the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics and may lead to Anderson localisation in Fock space [1,2]. Furthermore, the system features an unusual many-body localisation scenario in the sense that the it permits a mapping to fermions subject to non-local and disordered interactions. I will discuss the time-evolution of the entanglement entropy and population imbalance and will analyse the level-spacing statistics for this peculiar setting [3]. [1] M. Marcuzzi, J. Minar, D. Barredo, S. de Leseleuc, H. Labuhn, T. Lahaye, A. Browaeys, E. Levi and I. Lesanovsky, Facilitation dynamics and localization phenomena in Rydberg lattice gases with position disorder, Physical Review Letters 118, 063606 (2017) [2] M. Ostmann, M. Marcuzzi, J. Minár and I. Lesanovsky, Synthetic lattices, flat bands and localization in Rydberg quantum simulators, arXiv:1802.00379, Quantum Science and Technology (2019) [3] M. Ostmann, M. Marcuzzi, J.P. Garrahan and I. Lesanovsky, Localization in spin chains with facilitation constraints and disordered interactions, arXiv:1811.01667

Motivated by the presence of Ising transitions that take place entirely in the singlet sector of frustrated spin-1/2 ladders and spin-1 chains, we study two types of effective dimer models on ladders, a quantum dimer model and a quantum loop model. Building on the constraints imposed on the dimers, we develop a Density Matrix Renormalization Group algorithm that takes full advantage of the relatively small Hilbert space that only grows as Fibonacci number. We further show that both models can be mapped rigorously onto a hard-boson model first studied by Fendley, Sengupta and Sachdev [Phys. Rev. B 69, 075106 (2004)], and combining early results with recent results obtained with the present algorithm on this hard-boson model [arXiv:1808.08990], we discuss the full phase diagram of these quantum dimer and quantum loop models, with special emphasis on the phase transitions. We study systems with up to 9'000 sites and calculate the correlation length and the wave-vector of the incommensurate short-range correlations with unprecedented accuracy. We provide strong numerical evidence that there is an intermediate floating phase far enough from the integrable Potts point, while in its vicinity, our numerical data are consistent with a unique transition in the Huse-Fisher chiral universality class. Moreover, using conformal field theory, we fully characterize the Ising transition and the tricritical Ising end point, with a complete analysis of the boundary-field correspondence for the tricritical Ising point including partially polarized edges. Finally, we show that the Fibonacci anyon chain is exactly equivalent to special critical points of these models.

Out-of-time-ordered correlators (OTOCs) describe information scrambling under unitary time evolution and provide a useful probe of the emergence of quantum chaos. We calculate OTOCs for a model of disorder-free localization whose exact solubility allows us to study long-time behaviour in large systems. The model consists of fermions and spins minimally coupled, and generates dynamically its own disorder, which gives rise to localization of the fermionic degrees of freedom. Remarkably, we observe logarithmic spreading of correlations, qualitatively different to both thermalizing and Anderson localized systems. Rather, such behaviour is normally taken as a signature of many-body localization, so that our findings for an essentially non-interacting model are surprising. We provide an explanation for this unusual behaviour and suggest a novel Loschmidt echo protocol as a probe of correlation spreading.

We have been working on a quantum spin ice candidate Pr2Zr2O7 and present our recent work on the experimental observation of the metamagnetic transition under a field along the diagonal [111] direction, which separates a low-field spin liquid state and a polarized state. We examine the possibilities of hypothetical emergent excitations proposed in the quantum spin ice manifold and beyond.

I will report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet MgCr$_2$O$_4$ in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all the details of the dynamic magnetic response. This work demonstrates that the magnetic excitations in paramagnetic MgCr$_2$O$_4$ are faithfully represented in the entire Brillouin zone by a theory of magnons propagating in a highly-correlated paramagnetic background. I will discuss the relevance of this result to other pyrochlore antiferromagnets and to the general problem of determining the nature of magnetic excitations in spin-liquids from experimental data alone. Supported by the U.S. Department of Energy under award DE-SC-0018660.

The Heisenberg antiferromagnet with uniform nearest neighbour exchange on the pyrochlore lattice has a ground state that is macroscopically degenerate in the classical limit, and the degrees of freedom within the ground state manifold form an emergent gauge field. Weak exchange randomness lifts this ground state degeneracy and leads to spin glass freezing at a temperature scale set by the disorder. We discuss the low-energy excitations in this frozen state. Since the frozen state spontaneously breaks symmetry under global spin rotations, these excitations are expected to be Goldstone modes. In addition, to be low energy modes, they must be excitations of the emergent gauge field, which is distinguished from the one arising in spin ice materials because it has an intrinsic dynamics inherited from the precessional dynamics of Heisenberg spins. We show how the standard Halperin-Saslow theory of Goldstone modes in a spin glass must be modified to describe this constrained dynamics.

Quantum spin liquids (QSL's) have traditionally been discussed as states which do not break any symmetry, and so do not undergo any (conventional) thermodynamic phase transition. A ready-made language for such states was found in lattice gauge theory; within this picture, where a local constraint leads to a local "gauge" symmetry, Landau-like phase transitions are explicitly forbidden, and the properties of the spin liquid follow from its emergent gauge structure. Famous examples of this type include Kitaev's toric code, which can realise a Z2 lattice gauge theory, and quantum spin ice, a QSL described by a U(1) lattice gauge theory. Both are characterised by a high degree of entanglement, and fractionalised, topological, spin excitations. Quantum spin nematics, in contrast, are states which explicitly break spin-rotation symmetry, through a local, quadrupolar order parameter. And within the usual paradigm, these states would not be expected to display any of the magical properties of QSL's. In this talk we revisit this expectation, and explore the curious connection between QSL's and quantum spin nematics, as uncovered in projected wave functions for spin liquids on the triangular lattice [1], complimentary studies of square-lattice frustrated ferromagnets [2], and numerical calculations for quantum spin ice with frustrated transverse exchange [3]. In all of these cases, there is evidence that broken spin-rotation symmetry can coexist with the fractionalised excitations and long-range entanglement characteristic of a QSL. [1] T. Grover et al., Phys. Rev B 81, 245121 (2010) [2] R. Shindou et al. Phys. Rev B 84, 134414 (2011) [3] O. Benton et al., Phys. Rev. Lett. 121, 067201 (2018)

The exotic behaviour of quantum spin liquids in bilinear Hamiltonians is often underpinned by perturbative ring exchange processes that induce matrix elements between classically degenerate configurations. In this talk, I will discuss a novel semiclassical numerical method that allows to achieve unprecedented insight into the thermodynamic as well as spectral properties of these systems, and demonstrate its capabilities by applying to quantum spin ice. First, we obtain photonic normal modes in excellent agreement with large-$S$ field theory predictions. We then use the method to study gapped vortices of the emergent magnetic field that are analogous to visons, and obtain their bare energy cost and long ranged Coulomb interaction. In addition, we investigate their thermodynamics in the presence of a thermal bath of photons. Contrary to the behaviour of spinons in classical spin ice, we find that visons form a weak electrolyte: Their strong interaction makes the energy cost of a bound pair lower than that of an isolated vison, leading to a qualitatively different temperature dependence of the pinch points in the emergent magnetic field. Additionally, strong interactions between visons and the thermal bath of photons appear to reduce the creation energy of the former, suggesting a possible hybridisation between the two excitations in quantum spin ice. We close by commenting on the general applicability of the method to other quantum spin liquids and quantum dimer models.

We discuss some recent results indicating the absence of unbounded energy absorption (infinite-T local thermalization) in a periodically driven interacting spin chain. The non-thermal behaviour arises sharply above a threshold value of the drive amplitude. The freezing is attributed to the emergence of a local conserved quantity. Ref: Phys. Rev. B 97, 245122 (2018).