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arXiv:2508.16275 · Physical review. B./Physical review. B

Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian

Tian-Shu Deng, Fan Yang

Published Dec 12, 2025• 2 citations
arXivHTMLPDF

Abstract

We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form throughout the dynamics. By employing the modular Hamiltonian framework, we rigorously demonstrate that the $\rm{Z}_2$ topological invariant characterizing steady states in one-dimensional class D systems is exclusively dependent on the dissipation operators, rather than the system Hamiltonian. Through a sudden quench protocol where the system evolves from the steady state of one Lindbladian to another, we reveal that topological transitions can occur at analytically predictable critical times, even when the initial and final steady states share identical topological indices. These transitions are shown, both analytically and numerically, to depend solely on dissipation parameters. Entanglement spectrum analysis demonstrates bulk-edge correspondence in non-equilibrium density matrices via coexisting single-particle gap closures (periodic boundaries) and topologically protected zero modes (open boundaries), directly underpinning the detection of dissipation-induced topology in quantum simulators.

DOI
10.1103/3wcr-sxtz

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We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form throughout the dynamics. By employing the modular Hamiltonian framework, we rigorously demonstrate that the Z2\rm{Z}_2Z2​ topological invariant characterizing steady states in one-dimensional class D systems is exclusively dependent on the dissipation operators, rather than the system Hamiltonian. Through a sudden quench protocol where the system evolves from the steady state of one Lindbladian to another, we reveal that topological transitions can occur at analytically predictable critical times, even when the initial and final steady states share identical topological indices. These transitions are shown, both analytically and numerically, to depend solely on dissipation parameters. Entanglement spectrum analysis demonstrates bulk-edge correspondence in non-equilibrium density matrices via coexisting single-particle gap closures (periodic boundaries) and topologically protected zero modes (open boundaries), directly underpinning the detection of dissipation-induced topology in quantum simulators.
Abstract The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution. We solve this problem for the fermionic Gaussian state and for the modular Hamiltonian being a quadratic operator of a set of fermionic operators. When these conditions are satisfied, along with a nontrivial topological classification of the symmetry class of the modular Hamiltonian, a topological transition can occur as time evolves. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class with U (1) symmetry and the DIII class without U (1) symmetry. By a finite size scaling, we show that this density matrix topology transition occurs at a finite time. We also present the physical signature of this transition.
Dynamical quantum phase transitions occur in dynamically evolving quantum systems when nonanalyticities occur at critical times in the return rate, a dynamical analog of the free energy. This extension of the concept of phase transitions can be brought into contact with another, namely, that of topological phase transitions in which the phase transition is marked by a change in a topological invariant. Following a quantum quench dynamical quantum phase transitions can happen in topological matter, a fact which has already been explored in one-dimensional topological insulators and in two-dimensional Chern insulators. Additionally, in one-dimensional systems a dynamical bulk boundary correspondence has been seen, related to the periodic appearance of zero modes of the Loschmidt echo itself. Here we extend both of these concepts to two-dimensional higher-order topological matter in which the topologically protected boundary modes are corner modes. We consider a minimal model which encompasses all possible forms of higher-order topology in two-dimensional topological band structures. We find that dynamical quantum phase transitions can still occur, and can occur for quenches which cross both bulk and boundary gap closings. Furthermore, a dynamical bulk boundary correspondence is also found, which takes a different form to that in one dimension.
The development of non-Hermitian topological band theory has led to observations of novel topological phenomena in effectively classical, driven, and dissipative systems. However, for open quantum many-body systems, the absence of a ground state presents a challenge to define robust signatures of non-Hermitian topology. We show that such a signature is provided by crossings in the time evolution of the entanglement spectrum. These crossings occur in quenches from the trivial to the topological phase of a driven-dissipative Kitaev chain that is described by a Markovian quantum master equation in Lindblad form. At the topological transition, which can be crossed either by changing parameters of the Hamiltonian of the system or by increasing the strength of dissipation, the timescale at which the first entanglement spectrum crossing occurs diverges with a dynamical critical exponent of $\ensuremath{\epsilon}=1/2$. We corroborate these numerical findings with an exact analytical solution of the quench dynamics for a spectrally flat postquench Liouvillian. This exact solution suggests an interpretation of the topological quench dynamics as a fermion parity pump. Our work thus reveals signatures of non-Hermitian topology that are unique to quantum many-body systems and cannot be emulated in classical simulators of non-Hermitian wave physics.
Topological order offers possibilities for processing quantum information that can be immune to imperfections. However, the question of its stability out of equilibrium is relevant for experiments, where coupling to an environment is unavoidable. In this work, we demonstrate the robustness of certain aspects of Z 2 × Z 2 symmetry-protected topological (SPT) order against a wide class of dissipation channels in the Lindblad and quantum trajectory formalisms of an open quantum system. This is illustrated using the one-dimensional Z X Z cluster Hamiltonian along with Pauli-string jump operators. We show that certain choices of dissipation retaining strong symmetries support a steady-state manifold consisting of two nonlocal qubits and for Hamiltonian perturbations preserving the global symmetry, states in this manifold remain metastable. In contrast, this metastability is destroyed upon breaking the above-mentioned symmetry. While the localized qubits of the cluster Hamiltonian are not conserved by the Lindbladian evolution, they do correspond to weak symmetries and thus retain a memory of their initial state at all times in the quantum trajectories. We utilize this feature to construct protocols to retrieve the quantum information either by monitoring jumps or error mitigation. Our work thus proposes a novel framework to study the dynamics of dissipative SPT phases and opens up the possibility of engineering entangled states relevant to quantum information processing. Published by the American Physical Society 2024
We study dissipative phase transitions in a system of two coupled fully-connected quantum Ising models interacting with an environment. The dynamics is governed by a Lindblad master equation combining coherent unitary evolution and incoherent dissipative processes, where the unitary part is described within a self-consistent mean-field framework effectively acting on the local Hilbert space of two coupled spins at each site. We analyze two fundamentally different classes of dissipators. In the first case, the jump operators are defined in the instantaneous eigenbasis of the mean-field Hamiltonian and satisfy a detailed-balance condition. In this setting, the relaxation dynamics depends strongly on the quench protocol: a parametric quench of the Hamiltonian leads to conventional relaxation, whereas a temperature quench gives rise to a dynamical phase transition characterized by nonanalytic behavior in time. Yet, in both cases, the system relaxes toward a steady state determined solely by the post-quench parameters and the bath temperature, which closely resembles a thermal Gibbs state of the mean-field Hamiltonian. As a result, the dissipative phase transition occurs at a critical point consistent with the corresponding equilibrium transition. In contrast, when the dissipators are realized via local spin raising and lowering operators, the steady state is genuinely nonequilibrium, leading to a significantly richer phase diagram. In particular, for sufficiently strong system-bath coupling, we observe a reentrant phase featuring a symmetry-broken region bounded by two continuous dissipative phase transitions. Our results evidence how the structure of dissipative processes controls the emergence of equilibrium-like versus genuinely nonequilibrium critical behavior in open quantum systems.
We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the system's density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms which include local pumping and decay of particles.