The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. Could this be different when the dissipation is engineered to drive the system into a nontrivial quantum coherent steady state? In this work we shed light on this issue by studying the effect of disorder on recently introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady-state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite-size scaling methods we show that the critical exponent $\ensuremath{\nu}$ describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the nondissipative part of the dynamics. This indicates a different type of nonequilibrium quantum critical universality class accessible in cold-atom experiments.
The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. Could this be different when the dissipation is engineered to drive the system into a nontrivial quantum coherent steady state? In this work we shed light on this issue by studying the effect of disorder on recently introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady-state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite-size scaling methods we show that the critical exponent \ensuremathν describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the nondissipative part of the dynamics. This indicates a different type of nonequilibrium quantum critical universality class accessible in cold-atom experiments.
The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. In this work we shed new light on this issue by studying the effect of disorder on recently-introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite size scaling methods we show that the critical exponent ν describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the non-dissipative part of the dynamics. This indicates a new nonequilibrium quantum critical universality class accessible in cold-atom experiments.
We investigate the localization and topological properties of the nonequilibrium steady state (NESS) in a one-dimensional homogeneous system. Our results demonstrate that, despite the absence of disorder in the initial system, the NESS can exhibit localization under bond dissipation. These dissipation-driven localization and delocalization phenomena are clearly distinguished using Wigner distributions. Furthermore, we find that the initial localization characteristics of the system significantly influence the localization properties of the NESS. Drawing upon the concept of Bose-Einstein condensate broadening in cold-atom experiments, along with experimental data, we systematically characterize the impact of bond dissipation and disorder on the localization and topological properties of the NESS. The phase diagram reveals that the NESS can be topologically nontrivial even when the initial system is topologically trivial, and that the topological triviality of the initial system strengthens the topological nontriviality of the NESS. This work provides insights into the localization and topological phase transitions in homogeneous systems induced by bond dissipation and disorder.
Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantum-coherent many-body phenomena, and much effort is often devoted to their elimination. Recently this approach has changed: It has been realized that driven-dissipative dynamics could be used as a resource. By proper engineering of the reservoirs and their couplings to a system, one may drive the system towards desired quantum-correlated steady states, even in the absence of internal Hamiltonian dynamics. An intriguing category of equilibrium many-particle phases are those which are distinguished by topology rather than by symmetry. A natural question thus arises: which of these topological states can be achieved as the result of dissipative Lindblad-type (Markovian) evolution? Beside its fundamental importance, it may offer novel routes to the realization of topologically-nontrivial states in quantum simulators, especially ultracold atomic gases. Here I give a general answer for Gaussian states and quadratic Lindblad evolution, mostly concentrating on the example of 2D Chern insulator states. I prove a no-go theorem stating that a finite-range Lindbladian cannot induce finite-rate exponential decay towards a unique topological pure state above 1D. I construct a recipe for creating such state by exponentially-local dynamics, or a mixed state arbitrarily close to the desired pure one via finite-range dynamics. I also address the cold-atom realization, classification, and detection of these states. Extensions to other types of topological insulators and superconductors are also discussed.
The Anderson localization transition is one of the most well studied examples of a zero temperature quantum phase transition. On the other hand, many open questions remain about the phenomenology of disordered systems driven far out of equilibrium. Here we study the localization transition in the prototypical three-dimensional, noninteracting Anderson model when the system is driven at its boundaries to induce a current carrying nonequilibrium steady state. Recently we showed that the diffusive phase of this model exhibits extensive mutual information of its nonequilibrium steady-state density matrix. We show that this extensive scaling persists in the entanglement and at the localization critical point, before crossing over to a short-range (area-law) scaling in the localized phase. We introduce an entanglement witness for fermionic states that we name the mutual coherence, which, for fermionic Gaussian states, is also a lower bound on the mutual information. Through a combination of analytical arguments and numerics, we determine the finite-size scaling of the mutual coherence across the transition. These results further develop the notion of entanglement phase transitions in open systems, with direct implications for driven many-body localized systems, as well as experimental studies of driven-disordered systems.
This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude. In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models. Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition. The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.
We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field $\mathbit{H}=H(sin\ensuremath{\theta}cos\ensuremath{\phi},sin\ensuremath{\theta}sin\ensuremath{\phi},cos\ensuremath{\theta})$ induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for $\ensuremath{\alpha}<1$. We report a divergence of the Berry curvature at ${\ensuremath{\alpha}}_{c}=1$ for magnetic fields aligned along the equator $\ensuremath{\theta}=\ensuremath{\pi}/2$. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs at the localization Kosterlitz-Thouless quantum phase transition in this model. Recent experiments in quantum circuits have engineered nonequilibrium protocols to access topological properties from a measurement of a dynamical Chern number defined via the out-of-equilibrium spin expectation values. Applying a numerically exact stochastic Schr\"odinger approach we find that, for a fixed field sweep velocity $\ensuremath{\theta}(t)=vt$, the bath induces a crossover from (quasi)adiabatic to nonadiabatic dynamical behavior when the spin bath coupling $\ensuremath{\alpha}$ increases. We also investigate the particular regime $H/{\ensuremath{\omega}}_{c}\ensuremath{\ll}v/H\ensuremath{\ll}1$ with large bath cutoff frequency ${\ensuremath{\omega}}_{c}$, where the dynamical Chern number vanishes already at $\ensuremath{\alpha}=1/2$. In this regime, the mapping to an interacting resonance level model enables us to analytically describe the behavior of the dynamical Chern number in the vicinity of $\ensuremath{\alpha}=1/2$. We further provide an intuitive physical explanation of the bath-induced breakdown of adiabaticity in analogy to the Faraday effect in electromagnetism. We demonstrate that the driving of the spin leads to the production of a large number of bosonic excitations in the bath, which strongly affect the spin dynamics. Finally, we quantify the spin-bath entanglement and formulate an analogy with an effective model at thermal equilibrium.