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arXiv:2008.11727 · Physical review. B./Physical review. B

Entanglement transitions as a probe of quasiparticles and quantum thermalization

Tsung-Cheng Lu, Tarun Grover

Published Dec 3, 2020• 24 citations
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Abstract

The authors find that the entanglement between two subsystems in tripartite quantum states can reveal novel aspects of quantum thermalization. In particular, it can probe the presence or absence of long-lived quasiparticles. Systems without quasiparticles exhibit an ``entanglement transition'' from area to volume law as one tunes the subsystem volume fraction within a single representative state, a feature invisible in conventional schemes based on bipartite entanglement. Such a transition is absent in systems with quasiparticles.

DOI
10.1103/physrevb.102.235110

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The authors find that the entanglement between two subsystems in tripartite quantum states can reveal novel aspects of quantum thermalization. In particular, it can probe the presence or absence of long-lived quasiparticles. Systems without quasiparticles exhibit an ``entanglement transition'' from area to volume law as one tunes the subsystem volume fraction within a single representative state, a feature invisible in conventional schemes based on bipartite entanglement. Such a transition is absent in systems with quasiparticles.
Quantum information tends to spread out in interacting systems, leading to thermalization as characterized by the volume-law entropy of entanglement, while local measurements that extract classical information of the state tend to interrupt the propagation of information and reduce the entanglement entropy. Can entanglement sustain repeated measurements? The authors address this question in a toy hybrid-circuit model, where qubits undergo both unitary time evolution and sporadic local measurements. The phase diagram features a stable volume-law phase of entanglement for weak measurements and an area-law phase for strong measurements. The two domains in the diagram are separated by a single second-order phase transition. Characterization of both phases as well as of the critical point are presented.
The scaling law of entanglement entropy could undergo qualitative changes during the nonunitary evolution of a quantum many-body system. In this work, we uncover such entanglement phase transitions for free fermions in one-dimensional non-Hermitian quasicrystals (NHQCs). We identify two types of entanglement transitions with different scaling laws and critical behaviors due to the interplay between non-Hermitian effects and quasiperiodic potentials. The first type represents a typical volume-law to area-law transition, which happens together with a PT-symmetry breaking and a localization transition. The second type features an abnormal log-law to area-law transition, which is mediated by a critical phase with a volume-law scaling in the steady-state entanglement entropy. These entangling phases and transitions are demonstrated in two representative models of noninteracting NHQCs. Our results thus advance the study of entanglement transitions in non-Hermitian disordered systems and further disclose the rich entanglement patterns in NHQCs.
Thermal equilibrium in quantum many-body systems can be fully described by pure quantum states as far as local observables are concerned, while the conventional description of it is based on mixed-state ensembles.The thermodynamic entropy, in that case, is identified with the entanglement entropy of small subsystems.It scales with the size of the subsystem, which is called the volume law of entanglement.When the size of the subsystem increases, however, the correspondence between thermal and entanglement entropies fails and there appears a quantum correction to the simple volume-law scaling.Explicating the scaling of the entanglement entropy with the subsystem size is hence of great importance in connecting quantum physics to thermodynamics as well as analyzing recent experiments on ultracold atoms.In this thesis, we study the volume law of entanglement for pure quantum states representing thermal equilibrium.We derive an analytic formula of the volume law of entanglement for a certain class of pure states called canonical Thermal Pure Quantum (cTPQ) states which represent thermal equilibrium.We illustrate an advantage of the formula by numerically calculating the entanglement entropy of the cTPQ states and applying the formula to it.Furthermore, we argue that our formula universally applies to any sufficiently scrambled pure state, even if the state is not thermal.We consider two examples of such scrambled states, namely, stationary pure states after quantum quench and energy eigenstates of general Hamiltonians with and without integrability.The entanglement entropy of the former states, including actual experimental data in ultracold atoms, is in an excellent agreement with our formula as long as the states are scrambled.For the latter states, we find that our formula works as a good fitting function in non-integrable models to extract information in the thermodynamic limit from finite size systems.We also show that our formula can distinguish eigenstates of integrable models from non-integrable ones.4.3.1 Review of result by Lu and Grover for eigenstates of non-integrable models . . . . . . . . . . . .
Measurement-only circuits provide a minimal setting in which repeated local projections can either generate or suppress many-body entanglement, giving rise to measurement-induced phase transitions and dynamical regimes, that might have no unitary counterpart. Here we investigate entanglement and information transitions in one-dimensional measurement-only Clifford circuits with long-range two-qubit parity checks. By tuning both the measurement range and density per layer, we uncover a broad set of phases whose classification requires probes beyond entanglement entropy, such as mutual information, tripartite mutual information, purification from an ancilla, and Bell-cluster statistics. We map phase diagrams using large-scale Clifford simulations for two protocols: a random-basis design in which each measurement is randomly chosen from {XX,YY,ZZ}\lbrace XX,YY,ZZ \rbrace{XX,YY,ZZ}, and a single-basis design in which the basis is fixed within each layer but varies between layers, hence introducing more structure to the circuit. We map the trajectory-averaged entanglement entropy to a two-dimensional statistical mechanics model by extending a replica-based method to random-basis measurement-only circuits, and show that a continuous-time limit yields an effective long-range XX hamiltonian in the steady state. This connection links the observed volume-law to sub-volume-law entanglement transition to the boundary between a continuous symmetry broken phase and a critical XY phase. Strikingly, in structured (single-basis) circuits we find a phase in which volume-law and long-range entanglement coexists with rapid, size-independent purification of an ancilla qubit, and the absence of scrambling, highlighting measurement-only circuits as a promising route to efficiently preparing highly entangled and technologically useful quantum states.
Thermalization plays a central role in out-of-equilibrium physics of ultracold atoms or electronic transport phenomena. On the other hand, entanglement concepts have proven to be extremely useful to investigate quantum phases of matter. Here, it is argued that bipartite entanglement measures provide key information on out-of-equilibrium states and might therefore offer stringent thermalization criteria. This is illustrated by considering a global quench in an (extended) XXZ\mathit{XXZ}XXZ spin-1/2 chain across its (zero-temperature) quantum critical point. A nonlocal bipartition of the chain preserving translation symmetry is proposed. The time evolution after the quench of the reduced density matrix of the half-system is computed and its associated (time-dependent) entanglement spectrum is analyzed. Generically, the corresponding entanglement entropy quickly reaches a ``plateau'' after a short transient regime. However, in the case of the integrable XXZ\mathit{XXZ}XXZ chain, the low-energy entanglement spectrum still reveals strong time fluctuations. In addition, its infinite-time average shows strong deviations from the spectrum of a Boltzmann thermal density matrix. In contrast, when the integrability of the model is broken (by small next-nearest-neighbor couplings), the entanglement spectra of the time average and thermal density matrices become remarkably similar.