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arXiv:2008.00996 · Physical Review Research

Activity-induced phase transition in a quantum many-body system

Kyosuke Adachi, Kazuaki Takasan, Kyogo Kawaguchi

Published Mar 11, 2022• 26 citations
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Abstract

A crowd of nonequilibrium entities can show phase transition behaviors that are prohibited in conventional equilibrium setups. An interesting question is whether similar activity-driven phase transitions also occur in pure quantum systems. Here we investigate a classical anisotropic lattice gas model that undergoes motility-induced phase separation and extend the model to the quantum regime. The resulting model is a quantum many-body model that undergoes quantum phase transitions induced by non-Hermiticity. The quantum phase diagram includes active phase transitions involving phase separation, microphase separation, and flocking. The quantum phase transitions are identified as the transitions of dynamical paths in the classical kinetics upon the application of biasing fields. Our approach sheds light on the useful connection between classical nonequilibrium kinetics and non-Hermitian quantum physics.

DOI
10.1103/physrevresearch.4.013194

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A crowd of nonequilibrium entities can show phase transition behaviors that are prohibited in conventional equilibrium setups. An interesting question is whether similar activity-driven phase transitions also occur in pure quantum systems. Here we investigate a classical anisotropic lattice gas model that undergoes motility-induced phase separation and extend the model to the quantum regime. The resulting model is a quantum many-body model that undergoes quantum phase transitions induced by non-Hermiticity. The quantum phase diagram includes active phase transitions involving phase separation, microphase separation, and flocking. The quantum phase transitions are identified as the transitions of dynamical paths in the classical kinetics upon the application of biasing fields. Our approach sheds light on the useful connection between classical nonequilibrium kinetics and non-Hermitian quantum physics.
Motility-induced phase separation (MIPS) describes a central clustering phenomenon in active matter systems where particles spontaneously separate into dense and dilute phases even in the absence of interparticle attractive forces. Recent theoretical and experimental efforts have taken the first steps to extend active matter concepts to the quantum level. However, whether a genuine quantum analog of MIPS exists and how quantum coherence would compete or cooperate with the dissipative self-propulsion has remained open so far. Here, we provide evidence that quantum MIPS can occur in a model of active hard-core bosons in one dimension. Our model yields superlinear number fluctuations characteristic of MIPS, leading to microphase separation with large but finite cluster size. Adding nearest-neighbor repulsive interactions, we find numerical evidence for restoring genuine phase separation with a divergent correlation length. Crucially, the clustered steady states maintain a long-distance quantum coherence, revealing a genuinely quantum feature with no classical counterpart. These results provide a foundation for exploring quantum MIPS and suggest that the coherence-activity interplay can generate new types of nonequilibrium quantum states.
Abstract Non-Hermitian (NH) quantum system recently have attracted a lots of attentions theoretically and experimentally. However, the results based on the single-particle picture may not apply to understand the property of NH many-body system. How the property of quantum many-body system especially the phase transition will be affected by the non-Hermiticity remains unclear. Here we study NH quantum contact process (QCP) model, whose effective Hamiltonian is derived from Lindbladian master equation. We show that there is a continuous phase transition induced by the non-Hermiticity in QCP. We also determine the critical exponents β of order parameter, γ of susceptibility and study the correlation and entanglement near phase transition point. We observe that the order parameter and susceptibility display infinitely singularity even for finite size system, since non-Hermiticity endow many-body system with different singular behavior from classical phase transition. Moreover our results show that the phase transition have no counterpart in Hermitian case and belongs to completely different universality class.
We study a non-Hermitian quantum many-body model in one dimension analogous to the Vicsek model or active spin models, and investigate its quantum phase transitions. The model consists of two-component hard-core bosons with ferromagnetic interactions and activity, i.e., spin-dependent asymmetric hopping. Numerical results show the emergence of a ferromagnetic order induced by the activity, a quantum counterpart of flocking, that even survives in the absence of ferromagnetic interaction. We confirm this phenomenon by proving that activity generally increases the ground-state energies of the paramagnetic states, whereas the ground-state energy of the ferromagnetic state does not change. By solving the two-particle case, we find that the effective alignment is caused by avoiding the bound-state formation due to the non-Hermitian skin effect in the paramagnetic state. We employ a two-site mean-field theory based on the two-particle result and qualitatively reproduce the phase diagram. We further numerically study a variant of our model with the hard-core condition relaxed, and confirm the robustness of ferromagnetic order emerging due to activity. Published by the American Physical Society 2024
We discuss an open driven-dissipative many-body system, in which the competition of unitary Hamiltonian and dissipative Liouvillian dynamics leads to a nonequilibrium phase transition. It shares features of a quantum phase transition in that it is interaction driven, and of a classical phase transition, in that the ordered phase is continuously connected to a thermal state. We characterize the phase diagram and the critical behavior at the phase transition approached as a function of time. We find a novel fluctuation induced dynamical instability, which occurs at long wavelength as a consequence of a subtle dissipative renormalization effect on the speed of sound.
In the context of closed quantum systems, when a system prepared in its ground state undergoes a sudden quench, the resulting Loschmidt echo can exhibit zeros, resembling the Fisher zeros in the theory of classical equilibrium phase transitions. These zeros lead to nonanalytical behavior of the corresponding rate function, which is referred to as the dynamical quantum phase transition (DQPT). In this paper, we investigate DQPTs in the context of open quantum systems that are coupled to both Markovian and non-Markovian dephasing baths via a conserved quantity. The general framework is corroborated by studying the nonequilibrium dynamics of a transverse-field Ising ring. Our paper might shed light on theoretical developments of DQPTs in the strong system-bath coupling regime.
Understanding the nonequilibrium behavior of quantum systems is a major goal of contemporary physics. Much research is currently focused on the dynamics of many-body systems in low-dimensional lattices following a quench, i.e., a sudden change of parameters. Already such a simple setting poses substantial theoretical challenges for the investigation of the real-time postquench quantum dynamics. In classical many-body systems, the Kolmogorov-Mehl-Johnson-Avrami model describes the phase transformation kinetics of a system that is quenched across a first-order phase transition. Here, we show that a similar approach can be applied for shedding light on the quench dynamics of an interacting gas of Rydberg atoms, which has become an important experimental platform for the investigation of quantum nonequilibrium effects. We are able to gain an analytical understanding of the time evolution following a sudden quench from an initial state devoid of Rydberg atoms and identify strikingly different behaviors of the excitation growth in the classical and quantum regimes. Our approach allows us to describe quenches near a nonequilibrium phase transition and provides an approximate analytical solution deep in the quantum domain.