Nonequilibrium Dark Space Phase Transition

Carollo, Federico; Lesanovsky, Igor

doi:10.1103/physrevlett.128.040603

“…Quantum effects can alter the universal properties of absorbing-state phase transitions. This has been shown for Markovian open quantum systems [22][23][24][25][26][27][28][29][30], for systems with kinetic constraints [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] and for the quantum contact process [38,46]. Quantum dissipative RD spin chains, where the diffusive motion is replaced by coherent hopping, have been investigated in Ref.…”

mentioning

confidence: 99%

Reaction-Limited Quantum Reaction-Diffusion Dynamics

Perfetto

¹

,

Carollo

²

,

Garrahan

³

et al. 2023

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We consider the quantum nonequilibrium dynamics of systems where fermionic particles coherently hop on a one-dimensional lattice and are subject to dissipative processes analogous to those of classical reaction-diffusion models. Particles can either annihilate in pairs, A + A → ∅, coagulate upon contact, A + A → A, and possibly also branch, A → A + A. In classical settings, the interplay between these processes and particle diffusion leads to critical dynamics as well as to absorbing-state phase transitions. Here, we analyze the impact of coherent hopping and of quantum superposition, focusing on the so-called reaction-limited regime. Here, spatial density fluctuations are quickly smoothed out due to fast hopping, which for classical systems is described by a mean-field approach. By exploiting the time-dependent generalized Gibbs ensemble method, we demonstrate that quantum coherence and destructive interference play a crucial role in these systems and are responsible for the emergence of locally protected dark states and collective behavior beyond mean-field. This can manifest both at stationarity and during the relaxation dynamics. Our analytical results highlight fundamental differences between classical nonequilibrium dynamics and their quantum counterpart and show that quantum effects indeed change collective universal behavior.

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“…A renormalization group analysis concludes that strong temporal and spatial fluctuations in the active phase smooths out the first order transition predicted by mean-field approximations [23]. Numerical simulations of a 50 site chain using a tensor network (iTEBD) algorithm report a continuous absorbing state phase transition and provide first estimates for the critical exponents of a new quantum contact universality class [24][25][26]. A machine learning approach, employed to pinpoint the critical region, followed by a tensor network and quantum jump Monte Carlo analysis also provide estimates for the critical exponents [27]; they find that only one (decay) exponent differs from the DP value, and only in the case where the system is initialized in a homogeneous, all active state.…”

Section: Introductionmentioning

confidence: 89%

Absorbing State Phase Transition with Clifford Circuits

Makki¹,

Lang²,

Büchler³

2023

Preprint

1

0

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The role of quantum fluctuations in modifying the critical behavior of non-equilibrium phase transitions is a fundamental but unsolved question. In this study, we examine the absorbing state phase transition of a 1D chain of qubits undergoing a contact process that involves both coherent and classical dynamics. We adopt a discrete-time quantum model with states that can be described in the stabilizer formalism, and therefore allows for an efficient simulation of large system sizes. The extracted critical exponents indicate that the absorbing state phase transition of this Clifford circuit model belongs to the directed percolation universality class. This suggests that the inclusion of quantum fluctuations does not necessarily alter the critical behavior of non-equilibrium phase transitions of purely classical systems. Finally, we extend our analysis to a non-Clifford circuit model, where a tentative scaling analysis in small systems reveals critical exponents that are also consistent with the directed percolation universality class.

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“…The dynamics is formulated in terms of the Markovian quantum master equation [42][43][44], where coherent-Hamiltonian hopping replaces stochastic diffusion while reactions are dissipative. These quantum RD models attract significant attention since they connect the physics of Markovian open quantum systems [45][46][47][48][49][50][51][52][53] to that of systems with kinetic constraints [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68]. From the experimental perspective, on the one hand, quantum RD systems naturally connect to cold-atomic experiments involving particle losses [69][70][71][72][73][74][75][76].…”

Section: Introductionmentioning

confidence: 99%

Quantum reaction-limited reaction–diffusion dynamics of noninteracting Bose gases

Rowlands,

Lesanovsky,

Perfetto

2024

New J. Phys.

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We investigate quantum reaction–diffusion (RD) systems in one-dimension with bosonic particles that coherently hop in a lattice, and when brought in range react dissipatively. Such reactions involve binary annihilation ( A + A → ∅ ) and coagulation ( A + A → A ) of particles at distance d. We consider the reaction-limited regime, where dissipative reactions take place at a rate that is small compared to that of coherent hopping. In classical RD systems, this regime is correctly captured by the mean-field approximation. In quantum RD systems, for noninteracting fermionic systems, the reaction-limited regime recently attracted considerable attention because it has been shown to give universal power law decay beyond mean field for the density of particles as a function of time. Here, we address the question whether such universal behavior is present also in the case of the noninteracting Bose gas. We show that beyond mean-field density decay for bosons is possible only for reactions that allow for destructive interference of different decay channels. Furthermore, we study an absorbing-state phase transition induced by the competition between branching A → A + A , decay A → ∅ and coagulation A + A → A . We find a stationary phase-diagram, where a first and a second-order transition line meet at a bicritical point which is described by tricritical directed percolation. These results show that quantum statistics significantly impact on both the stationary and the dynamical universal behavior of quantum RD systems.

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Nonequilibrium Dark Space Phase Transition

Cited by 11 publications

References 55 publications

Reaction-Limited Quantum Reaction-Diffusion Dynamics

Reaction-Limited Quantum Reaction-Diffusion Dynamics

Absorbing State Phase Transition with Clifford Circuits

Quantum reaction-limited reaction–diffusion dynamics of noninteracting Bose gases

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