Ergodicity Breaking and Anomalous Transport in Quantum Many-Body Systems

We consider interacting particles under the influence of a constant potential gradient, corresponding to Wannier-Stark localization in the noninteracting limit, on both a one-[1] and two-dimensional lattice. The eigenstate thermalization hypothesis in its strong formulation is violated even for arbitrarily weak tilts. Further, there is area-law rather than logarithmic growth of entanglement. This type of localization is therefore essentially different from disorder-driven many-body localization. [1] Elmer V. H. Doggen, Igor V. Gornyi, Dmitry G. Polyakov, Phys. Rev. B 103, L100202 (2021)

In this talk I will present a general mechanism for robust nonergodic behavior in the absence of disorder as a consequence of local constraints induced by gauge invariance. In particular, I will show that even genuinely interacting two-dimensional lattice gauge theories can become nonergodic. As a consequence this disorder-free localization scenario constitutes an ergodicity breaking mechanism even stronger than for inhomogeneous systems in the context of many-body localization, where nonergodicity in two dimensions has been argued to be unstable.

I will discuss several aspects of MBL with possible stress on -- the existence of MBL in the thermodynamic limit for short-range interacting models and the hints on it we obtain from different numerical approaches -- MBL with long range cavity mediated interactions -- Localization in disorder free potentials All three issues cannot be obviously properly addressed in a talk so a selection will be made later.

I will discuss my perspectives on where we are in our understanding (and lack thereof) of the “phase diagram” of many-body localization. I will focus on the “basic” cases of systems with quenched randomness, no global conservation laws, and only short-range interactions. Morningstar, Colmanerez, Khemani, Luitz, Huse, 2107.05642

I will give an overview of recent work on minimal models for quantum chaos and many-body localisation. The models are Floquet quantum circuits for lattice spin systems, in which time evolution is generated by unitary gates that couple neighbouring sites. In particular, I will discuss the circumstances in which a version of the so-called diagonal approximation (originally developed for the semiclassical limit in low-dimensional chaotic systems) can be applied to these systems. Within this framework I will show that the many-body delocalisation transition can be seen as a form of symmetry breaking transition, having many of the features generally associated with conventional phase transitions in classical statistical mechanical models. Joint work with Sam Garratt: Phys. Rev. X 11, 021051 (2021) [arXiv:2008.01697] and Phys. Rev. Lett. to appear [arXiv:2012.11580].

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the time-scale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n−multipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For n≥1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n+1. A simple theory based on Fermi's golden rule accounts for this behaviour. The quasiperiodic Thue-Morse sequence corresponds to the n→∞ limit, and accordingly exhibits an especially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host various non-equilibrium phases.

Recent years have uncovered many fascinating phenomena in non-equilibrium quantum systems. A paradigmatic example are many-body localized systems. Those systems do not reach equilibrium due to the localization of the constituent particles. Despite intensive research, many questions on many-body localization remain open, for instance, on the thermal-localized transition, their entanglement dynamics, and the stability against thermalizing perturbations. In this talk I will present our recent studies on many-body localization. The experiments take place with neutral atoms in a one-dimensional optical lattice. Microscopic control over the individual atoms and lattice sites allows us to prepare, evolve, and locally read out arbitrary quantum states. We observe several key characteristics, including the localization properties, the entanglement dynamics, the critical behavior at the thermal-localized transition, and the stability at a clean-disorder interface. Our results provide a new perspective on entanglement formation in non-equilibrium systems, and they provide a starting point for further studies on thermalization in strongly correlated systems.

Authors: P. Haldar, Sen Mu, N. Macé, B. Georgeot, J. Gong, M. Albert, C. Miniatura, and G. Lemarié Abstract: Periodically-driven quantum systems make it possible to reach stationary states with new emerging properties. However, this process is notoriously difficult in the presence of interactions because continuous energy exchanges generally boil the system to an infinite temperature featureless state. Here, we describe how to reach nontrivial states in a periodically-kicked Gross-Pitaevskii disordered system. One ingredient is crucial: both disorder and kick strengths should be weak enough to induce sufficiently narrow and well-separated Floquet bands. In this case, inter-band heating processes are strongly suppressed and the system can reach an exponentially long-lived prethermal plateau described by the Rayleigh-Jeans distribution. Saliently, the system can even undergo a wave condensation process or transit to a superfluid regime when its initial state has a sufficiently low total quasi-energy. These predictions could be tested in nonlinear optical experiments or with ultracold atoms.

Time-periodic Floquet drive is a powerful method to engineer quantum phases of matter, including fundamentally nonequilibrium states that cannot be realized in static Hamiltonian systems. A characteristic example is the anomalous Floquet topological insulator, which exhibits a unique topologically protected nonequilibrium transport phenomenon: nonadiabatic quantized charge pumping. We study the fate of this phenomenon in the presence of time-dependent noise, which breaks the protecting Floquet symmetry. Surprisingly, we find that the charge pumped per cycle remains quantized up to a finite noise amplitude. We trace this robustness of Floquet topology to an interplay between diffusion and Pauli blocking of the decay of chiral edge states.

Entanglement transitions in quantum dynamics present a novel class of phase transitions in non-equilibrium systems. When a many-body quantum system undergoes hybrid quantum dynamics, consisting of unitary evolution interspersed with monitored random measurements, the steady-state can exhibit a phase transition between volume- and area-law entanglement. It is known that for monitored circuits with Clifford unitaries in one dimension, their critical properties are close to those of 2D classical percolation. In this work we show more evidence of this correspondence in 1+1D and 2+1D circuits using a graph-state based simulation algorithm where the entanglement structure is encoded in an underlying graph, providing access to the geometric structure of entanglement. We precisely locate the critical point using the tripartite information, revealing area-law entanglement scaling at criticality in two dimensions. Entanglement structure of the stationary state is analysed, together with the purification dynamics, in order to extract bulk critical exponents, which match closely to percolation. We also find that critical exponents of entanglement clusters do not match those of surface percolation exponents. Our results shed more light on the relation and possible mapping between monitored Clifford models and percolating networks.

I will first give a short overview of generalised hydrodynamics (GHD), a hydrodynamic theory for many-body integrable systems. I will emphasise the wide applicability of GHD. For instance, it was introduced to describe the large-scale motion in quantum systems at finite densities, such as the Lieb-Liniger gas describing cold atoms. But it has a few predecessors, including the much studied soliton gases modelling wave turbulence in shallow water. I will overview how it can be seen as a hydrodynamic theory derived from the available conserved quantities and the local-entropy-maximisation principle, or as a kinetic theory for stable quasiparticles. In real situations, however, integrability is broken. I will then explain how to take into account the effects of homogeneous integrability breaking perturbations. GHD is modified by a thermalising term, with an explicit Green-Kubo-like formula, that evaluates to a Boltzmann collision integral for the quasiparticles of the integrable system.

Quantum simulation with ultracold atoms has opened the avenue to probe non-equilibrium quantum many body dynamics in new parameters regimes and with completeley new detection techniques. Specifically, we utilize the high-resolution, single-spin sensitive detection afforded by a quantum gas microscope to track the out-of-equilibrium dynamics of Heisenberg quantum magnets. In recent experiments, we have tracked the evolution of one-dimensional Heisenberg spin chains starting from initial spin-domain wall states. We demonstrate superdiffusive spin transport in this regime by monitoring the polarization transfer in the system over time. Additionally, by accessing the full counting statistics of transported spins, we find strong supporting evidence for the conjecture that transport in the XXZ chain at the Heisenberg point indeed falls in the KPZ universality class.

Classical hydrodynamics is a remarkably versatile description of the coarse-grained behaviour of many-particle systems once local equilibrium has been established. The form of the hydrodynamical equations is determined primarily by the conserved quantities present in a system. Some quantum spin chains are known to possess, even in the simplest cases, a greatly expanded set of conservation laws, and recent work suggests that these laws strongly modify collective spin dynamics, even at high temperature. Here, by probing the dynamical exponent of the one-dimensional Heisenberg antiferromagnet KCuF3 with neutron scattering, we find evidence that the spin dynamics are well described by the dynamical exponent z = 3/2, which is consistent with the recent theoretical conjecture that the dynamics of this quantum system are described by the Kardar–Parisi–Zhang universality class. This observation shows that low-energy inelastic neutron scattering at moderate temperatures can reveal the details of emergent quantum fluid properties like those arising in non-Fermi liquids in higher dimensions.

Driven quantum systems provide an intriguing landscape for studying novel phases of non-equilibrium matter. In this talk, I will describe recent advances, which predict the spontaneous breaking of time translation symmetry in periodically driven quantum systems. The resulting discrete time crystal exhibits collective oscillations that are quantized to an integer multiple of the drive period. Particular care will be taken to contextualize modern results on discrete time crystals with subharmonic oscillations that are commonplace in non-linear dynamical systems. Time permitting, I will survey recent experiments demonstrating the observation of time crystalline order in a variety of quantum simulation platforms.

An open quantum system is continuously “monitored” by its environment, so its dynamics consists of two competing processes: unitary evolution, which generates entanglement and generically leads to chaotic dynamics, and non-unitary operations resulting from measurements and noisy couplings to the environment, that tend to irreversibly destroy quantum information by revealing it. A minimal model that captures these competing processes consists of a quantum circuit made up of random unitary gates interlaced with local projective measurements. Remarkably, this minimal model undergoes a dynamical phase transition as the rate of measurements is increased. In this talk, I will introduce an exact replica statistical mechanics approach to this problem, and show that the transition is described by a CFT with central charge c=0. I will also present numerical results on the spectrum of this theory using a transfer matrix approach that indicate multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

TBA

I will discuss simple integrable models in discrete space-time lattice with non-abelian global SU(N) or Sp(N) symmetry Numerical investigations of spin transport in these models hint at KPZ universality with dynamical exponent z=3/2, irrespective of the underlying symmetry group.

A quantum jammed state can be seen as a state where the phase space available to particles shrinks to zero, an interpretation quite accurate in integrable systems, where stable quasiparticles scatter elastically. I consider the integrable dual folded XXZ model, which is equivalent to the XXZ model in the limit of large anisotropy. I show how to solve the model by means of a coordinate Bethe Ansatz that manifestly breaks translational symmetry and demonstrate the existence of exponentially many jammed states. In the second part of the talk I consider the effect of a jamming-breaking localised measurement in a jammed state. I show that jamming is locally restored, but local observables exhibit nontrivial time evolution on macroscopic, ballistic scales, without ever relaxing back to their initial values. [1] Lenart Zadnik, Maurizio Fagotti, "The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties", SciPost Phys. Core 4, 010 (2021). [2] Lenart Zadnik, Kemal Bidzhiev, Maurizio Fagotti, "The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with a minimal set of charges", SciPost Phys. 10, 099 (2021). [3] Kemal Bidzhiev, Maurizio Fagotti, and Lenart Zadnik, "Macroscopic effects of localised measurements in jammed states of quantum spin chains", arXiv:2108.03230 (2021).

Sometimes, very well-known models in interdisciplinary areas of physics can still reveal unexpected and interesting surprises. In this talk, I discuss the 1d Ising model in transverse and longitudinal fields: in the case of non-zero longitudinal field and far from the critical point, the model is known to be non-integrable. However, in the case of finite longitudinal field and weak transverse component, an unexpected richness of the dynamics emerges. The effective Hamiltonian exhibits fragmentation of the Hilbert space in exponentially many decoupled sectors: the sector where magnons are isolated turns out to be governed by an integrable Hamiltonian, first discovered by Alcaraz and Bariev in 1999. Due to the emergent integrability, transport in the isolated magnon sector shows ballistic features rather than the naively-expected diffusion: we construct the exact generalized hydrodynamics of the model, which shows a peculiar interaction-dependent behavior with a fractionalize magnetization transported by the carriers. Lastly, I briefly outline transport outside of the integrable sector. Reference: A. Bastianello, U. Borla, S. Moroz, arXiv:2108.04845 (2021)

I will introduce a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. This equation predicts entropy increase and thermal states as the only stationary states and it applies to any hydrodynamic system with any number of local, PT-symmetric conserved quantities, in arbitrary dimension. I will show how this implies thermalisation for a one-dimensional gas of trapped interacting bosons.

I will describe experiments with an array of 1D gases taken out of equilibrium with trap quenches. We measure the evolving distribution of rapidities and compare the observed evolution to generalized hydrodynamics (GHD). We find excellent agreement over many trap oscillation cycles, even for large quenches and when there are few atoms per 1D gas. I will also briefly discuss the result of a wavefunction quench, which compromises the validity of GHD approximations.

In an effort to address integrability breaking in cold gas experiments, we extend the integrable hydrodynamics of the Lieb-Liniger model with two additional components representing the population of atoms in the first and second transverse excited states, thus enabling a description of quasi-1D condensates [1]. Collisions between different components are accounted for through the inclusion of a Boltzmann-type collision integral in the hydrodynamic equation. Besides the theoretical concepts I will present experimental verification [1] of the extended GHD through non equilibrium dynamics and thermalization of a quantum Newton’s cradle [2]. [1] F. Moller et al., Phys. Rev. Lett. 126, 090602 (2021) [2] Chen Li et al., SciPost. Phys. 9, 058 (2020)

I will discuss the effects of weak perturbations on dynamics of integrable many-body systems. While in the thermodynamic limit already an infinitesimal perturbation causes transition from integrability to chaos, and diffusive transport, there can nevertheless be a remnant of integrability imprinted in the dependence of the diffusion constant on the perturbation strength. Specifically, for dilute impurities Matthiessen's rule, saying that the diffusion is proportional to the inverse density of impurities, has to be in general modified.

Exceptions to thermalization in quantum many-body systems provide interesting opportunities. Many-body localization, in which all states in the spectrum have area law entanglement, constitutes a strong violation of the eigenstate thermalization hypothesis, and quantum many-body scars instead give rise to a weak violation with a few nonthermal states embedded in a spectrum of thermal states. Here, we propose and demonstrate that one can similarly have a weak violation of many-body localization, in which one or a few states in a spectrum have above area law entanglement, while the rest of the states are many-body localized. We show that this can be achieved through a mechanism, in which emergent symmetry of the special states prevents many-body localization in these states. Reference: Phys. Rev. Lett. 125, 240401 (2020)

We study how interacting localized degrees of freedom are affected by slow thermal fluctuations that change the effective local disorder. We compute the time-averaged (annealed) conductance in the insulating regime and find three distinct insulating phases, separated by two sharp transitions. The first occurs between the deep non-resonating insulator and a rarely-resonating insulator (or intermittent metal). The average conductance is always dominated by rare temporal fluctuations. However, in the intermittent metal, they are so strong that the system becomes metallic for an exponentially small fraction of the time. A second transition occurs within that phase. At stronger disorder, there is a single optimal path providing the dominant contribution to the conductance at all times, but closer to delocalization, a transition to a phase with fluctuating paths occurs. This last phase displays the quantum analogon of configurational chaos in glassy systems, in that thermal fluctuations induce significant changes of the dominant decay channels. While in the insulator the annealed conductance is strictly bigger than the conductance with typical, frozen disorder, we show that the threshold to delocalization is insensitive to whether or not thermal fluctuations are admitted. This rules out a potential bistability, at fixed disorder, of a localized phase with suppressed internal fluctuations and a delocalized, internally fluctuating phase.

We show that dipole- and higher-moment conserving systems exhibit exotic dynamics when brought out of equilibrium. First, we show that the combination of locality and conservation laws yields an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. Second, we show that systems conserving higher moments of an associated global charge exhibit a slow subdiffusive transport. Modeling the time evolution as cellular automata for specific cases of dipole conservation, we numerically find distinct anomalous exponents of the late time relaxation for one- and two-dimensional systems. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions.

Despite its many successes, linear response has its limitations as a probe of correlated quantum matter. Nonlinear response, and specifically multidimensional coherent spectroscopy (MDCS), provides one way to overcome some of these limitations. MDCS, a staple tool in chemistry and atomic physics of few-body systems, probes higher-order multiple-time correlations of a near-equilibrium system. Experimental efforts are underway to extend this to a probe of both clean [1] and disordered [2] many-body systems, but the theoretical toolbox for computing nonlinear response in interacting quantum systems is primitive. In this talk, I will present two classes of problem where (asymptotically) exact calculations of nonlinear response are possible: (i) disordered systems in the asymptotic scaling regime of infinite-randomness fixed points, where MDCS accesses exponents that characterise the critical points and proximate Griffiths phases [3]; and (ii) interacting integrable systems in one dimension, where generalised hydrodynamics can be leveraged into a formalism to compute multipoint correlators that is exact in the Eulerian hydrodynamic limit, revealing distinctions between free and interacting integrable systems and providing recursive expressions for nonlinear Drude weights [4]. References: [1] J. Lu \textit{et al}, Phys. Rev. Lett. \textbf{118}, 207204 (2017). [2] F. Mahmood \textit{et al}, Nat. Phys. \textbf{17}, 627–631 (2021). [3] S.A. Parameswaran and S. Gopalakrishnan, Phys. Rev. Lett. \textbf{125}, 237601 (2020). [4] M. Fava,S. Biswas, S. Gopalakrishnan, R. Vasseur, and S.A. Parameswaran, arXiv: 2103.06899, to appear in PNAS (2021).

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dynamical phases can be defined in periodically driven many-body localized systems via the concept of eigenstate order. In eigenstate-ordered phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, wherein few select states can mask typical behavior. Here we implement a continuous family of tunable CPHASE gates on an array of superconducting qubits to experimentally observe an eigenstate-ordered DTC. We demonstrate the characteristic spatiotemporal response of a DTC for generic initial states. Our work employs a time-reversal protocol that discriminates external decoherence from intrinsic thermalization, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigen spectrum. In addition, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on current quantum processors.

In this talk, we will discuss a random-matrix approach to the description of disordered many-body systems and their Hilbert-space structure, mostly focusing on the slow dynamics in such models. As a generic example of this approach, we consider the static and the dynamical phases in a Rosenzweig-Porter random matrix ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the averaged survival probability may decay with time as a simple exponent, as a stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. We consider the mapping of the Anderson localization model on Random Regular Graph, the known proxy of MBL, onto the RP model and find exact values of the stretch-exponent kappa in the thermodynamic limit. Our theory allows to describe analytically the finite-size multifractality and to compute the critical length with the exponent 1 associated with it. Corresponding publication: I. M. Khaymovich and V. E. Kravtsov "Dynamical phases in a "multifractal" Rosenzweig-Porter model" [arxiv:2106.01965]

I combine a geometric perspective on Fock space with considerations from random-matrix theory to provide insights into quantum systems that obey an area law on entanglement induced by disorder or measurements. For instance, individual many-body-localized eigenstates are well approximated by a Slater determinant of single-particle orbitals, but the orbitals of different eigenstates in a given system display an imperfect degree of compatibility, close to that of completely random states. Such considerations also illuminate the strongly dressed nature of any emergent local conserved quantities, as well as the universal properties of such systems. Universality of Entanglement Transitions from Stroboscopic to Continuous Measurements M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. Lett. 125, 210602 (2020). Fock-space geometry and strong correlations in many-body localized systems Christian P. Chen and Henning Schomerus, arXiv:2107.05502 [cond-mat.dis-nn]. (2021) Random-matrix perspective on many-body entanglement with a finite localization length Marcin Szyniszewski and Henning Schomerus, Phys. Rev. Research 2, 032010(R) (2020). Entanglement transition from variable-strength weak measurements M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. B 100, 064204 (2019).

Taking the Hatano-Nelson model as a concrete example, we first consider how diffusion occurs in a non-Hermitian disordered system, and show that it is very different from the Hermitian case. Interestingly, a cascade like diffusion process of an initial wave packet as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in time in the interacting non-Hermitian model, revealing its non-monotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy.

The absence of thermalization in certain isolated many-body systems is of great fundamental interest and potential technological importance. However, it is not well understood how the interplay of disorder and interactions affects thermalization, especially in two dimensions (2D), and experiments on solid-state materials remain scarce. We report on the study of nonequilibrium dynamics exhibited after a rapid change of electron density $n_\mathrm{s}$, in two sets of disordered 2D electron systems in Si, poorly coupled to a thermal bath. In the low conductivity regime at low $n_\mathrm{s}$, we find that, while the dynamics is glassy in devices with the long-range Coulomb interaction, in the case of screened Coulomb interaction the thermalization is anomalously slow, consistent with the proximity to a many-body-localized (MBL) phase, i.e. the MBL-like, prethermal regime. Our results demonstrate that the MBL phase in a 2D electron system can be approached by tuning the interaction range, thus paving the way to further studies of the breakdown of thermalization and MBL in real materials.

Recent years have seen the development of isolated quantum simulator platforms capable of exploring interesting questions at the frontiers of many-body physics. We describe our platform, based on a chain of Ytterbium ions in a linear trap, and describe its capabilities, which include long-range spin-spin interactions and single-site manipulation and readout. We then describe some recent studies undertaken with this machine, focusing on two. The first is the observation of domain-wall confinement, in which the long-range interactions cause individual domain walls to become bound into meson-like quasiparticles. The second, observation of Stark many-body localization, in which a linearly increasing gradient halts thermalization in favor of a state similar to disorder-induced many-body localization. These results show some of the richness possible in non-thermalizing behavior, and we discuss possible relations between them and recently studied mechanisms for breaking ergodicity such as Hilbert space fragmentation.

We introduce a class of unitary circuits which are invariant under translations. In the limit of large local Hilbert space dimensions, we compute explicitly the spectral form factor, characterizing the spectral correlation of the model. We show that at time larger than the Thouless time, the random matrix behavior is recovered. Additionally, we identify a scaling function which characterize an extended transient regime towards the random matrix prediction. Compared with the inhomogeneous system, we identify logarithmic corrections which are the direct consequence of translation invariance. We discuss the generalization of these results to arbitrary chaotic model which have a translation symmetry.

We demonstrate that a broad class of interacting disorder-free systems, such as nodal semimetals (e.g. graphene, Weyl, nodal-line semimetals) and dilute interacting gases, can be mapped to non-interacting systems with quenched disorder. The interacting systems that allow for such a mapping include systems with a small single-particle density of states at the chemical potential (e.g. near a nodal point or a nodal line in a topological semimetal), which leads to a suppressed screening of the interactions. The established duality suggests a new approach for analytical and numerical studies of many-body phenomena in a class of interacting disorder-free systems by reducing them to single-particle problems. It allows one to predict, describe and classify many-body phenomena by mapping them to the effects known for disordered non-interacting systems. We illustrate the mapping by showing that clean semimetals with attractive interactions exhibit interaction-driven transitions at low temperatures in the same universality classes as the non-Anderson disorder-driven transitions predicted in high-dimensional non-interacting semimetals. Furthermore, we find a new non-Anderson disorder-driven transition dual to a previously known interaction-driven transition in clean bosonic gases. The established principle may also be used to classify and describe phase transitions in dissipative systems described by non-Hermitian Hamiltonians.