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arXiv:2410.05370

Entanglement, information and non-equilibrium phase transitions in long-range open quantum Ising chains

Daniel A. Paz, Benjamin Maves, Naushad Ahmad Kamar, Arghavan Safavi-Naini, Mohammad F. Maghrebi

Published Oct 7, 2024• 1 citation
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Abstract

Non-equilibrium phase transitions of open quantum systems generically exhibit diverging classical but not quantum correlations. Still entanglement -- characterizing the latter correlations -- can be sensitive to the phase transition. Furthermore, mutual information, bounding the total correlations, should exhibit critical scaling at the transition. In this work, we study these quantities in the steady state of open quantum Ising chains with power-law interactions (with the exponent $0\le α\le 3$) where spins are subject to spontaneous emission. The bulk of this paper is dedicated to a detailed analytical as well as numerical analysis of the infinite-range model ($α=0$), a model that is closely related to the paradigmatic open Dicke model. Our main findings are that the entanglement, while being finite, peaks, exhibits a kink and takes a universal value at the transition, while the mutual information exhibits critical scaling not only at the transition but well into the ordered phase, underscoring a hidden criticality that is not captured by (two-point) correlations. We consider three distinct entanglement measures: logarithmic negativity; quantum Fisher information; and, spin squeezing. Specifically, we show that the collective spin operator that maximizes the quantum Fisher information can be identified with the \textit{gapless} mode of the phase transition, while the squeezed direction is that of the \textit{gapped} mode. Finally, we investigate power-law interacting models using matrix product states where we find comparable bounds on squeezing even when no phase transition is expected (for larger $α$), thus the connection to the phase transition does not appear to hold for shorter-range interactions.

DOI
10.48550/arxiv.2410.05370

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We numerically investigate classical and quantum correlations in one-dimensional quantum critical systems. The infinite matrix product state (iMPS) representation is employed in order to consider an infinite-size spin chain. By using the infinite time-evolving block decimation algorithm, iMPS ground state wave functions are obtained at critical points for the transverse-field spin-1/21/21/2 XY model. From the ground state wave functions, we calculate classical and quantum correlations and mutual information. All of the correlations are found to exhibit a power-law decay with the increments of the lattice distance for both the transition lines of the Ising universality class and the Gaussian universality class. Such power-law scaling behaviors of the correlations manifest the existence of diversing correlation lengths, which means scale invariance. The critical features of the correlations can be characterized by introducing a critical exponent of the power-law decaying correlations. Similar to the critical exponent ηηη of the spin-spin correlation for the universality classes in the transverse-field XY model, we calculate the critical exponents of the two-spin classical and quantum correlations as well as that of the corresponding mutual information. All of the correlations have the same critical exponents, i.e., ηI=ηC=ηDη^{I}=η^{C}=η^{D}ηI=ηC=ηD at a critical point, where the superscripts III, CCC, and DDD stand for mutual information, classical correlation, and quantum correlation, respectively. Furthermore, the critical exponent ηηη of the spin-spin correlation is shown to relate to η=ηα/2η= η^α/2η=ηα/2 with α∈{I,C,D}α\in \{ I, C, D\}α∈{I,C,D}.
Entanglement exhibits universal behavior near the ground-state critical point where correlations are long ranged and the thermodynamic entropy is vanishing. On the other hand, a quantum quench imparts extensive energy and results in a build up of entropy, hence no critical behavior is expected at long times. In this work, we present a new paradigm in the quench dynamics of integrable spin chains which exhibit a ground-state order-disorder phase transition at a critical line. Specifically, we consider a quench along the critical line which displays a volume-law behavior of the entropy and exponentially decaying correlations; however, we show that quantum criticality is hidden in higher-order correlations and becomes manifest via measures such as the mutual information and logarithmic negativity. Furthermore, we showcase the scale invariance of the Rényi mutual information between disjoint regions as further evidence for genuine critical behavior. We attribute the emergent quantum criticality to the soft mode not getting excited in spite of the quench. Moreover, the results presented here are universal to models whose low-energy or long-wavelength dynamics are well described by a free-fermionic field theory. Our results are amenable to an experimental realization on different quantum simulator platforms, particularly the Rydberg simulators. Published by the American Physical Society 2024
In this paper, we investigate Quantum Phase Transitions (QPTs) in the long-range XXZ spin chain using two information-theoretic probes: The half-chain entanglement entropy and a witness of genuine multipartite nonlocality. Both quantities effectively identify the phase boundary, but exhibit distinct scaling behaviors: the entanglement entropy grows linearly with system size N, while the multipartite nonlocality increases exponentially, with [Formula: see text]. By independently tuning the power-law decay exponents of the transverse ([Formula: see text]) and longitudinal ([Formula: see text]) couplings, we uncover contrasting trends in the critical point [Formula: see text]: Increasing [Formula: see text] shifts it to larger values, while increasing [Formula: see text] shifts it to smaller ones. These monotonic and saturating dependencies are captured by an empirical exponential model, offering a compact and physically transparent description of the critical behavior. Our results highlight the crucial role of interaction range in driving criticality, with implications for engineered quantum systems and long-range entanglement control.
Abstract The theory of multipartite entanglement provides a robust framework for understanding complex phenomena in quantum many-body systems, while multipartite entanglement also serves as a key resource in numerous quantum information processing tasks. Using density matrix renormalization group calculations, we study the multipartite entanglement in one-dimensional quantum long-range ferromagnetic and antiferromagnetic Ising chains with algebraically decaying interactions 1/ r α , respectively. To quantitatively probe the system’s multipartite entanglement structure, we employ the quantum Fisher information (QFI). Our results reveal two key behaviors: as the system size increases, the QFI rises, while the multipartite entanglement density decreases and converges toward a constant value. The latter trend points to a fundamental constraint on entanglement distribution in the thermodynamic limit. We further discuss the effects of the magnetic field and the exponent α on the QFI. We find that the peak values of the QFI increase with increasing α . Additionally, the discontinuity in the QFI can be regarded as a powerful tool for characterizing quantum phase transitions in the systems.
We investigate phase transitions in the nonequilibrium dynamics of power-law interacting spin-1/2 bilayer XXZ models, which have recently been shown to allow generation of entanglement in the form of two-mode squeezing. We find a transition between a collective phase characterized by Heisenberg limited squeezing and a partially collective phase with scalable squeezing. We identify universal scaling of the squeezing dynamics in terms of system parameters and a divergent timescale, establishing these as distinct dynamical phases within the framework of nonequilibrium critical phenomena. Our Letter demonstrates a novel dynamical phase transition with potential applications in quantum sensing and quantum simulation in cold-atomic, molecular, or Rydberg platforms.
We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent α \\alpha , in regimes of direct interest for current trapped ion experiments. Using large-scale path integral Monte Carlo simulations, we investigate both the ground-state and the nonzero-temperature regimes. We identify the phase boundary of the ferromagnetic phase and obtain accurate estimates for the ferromagnetic-paramagnetic transition temperatures. We further determine the critical exponents of the respective transitions. Our results are in agreement with existing predictions for interaction exponents α > 1 \\alpha > 1 up to small deviations in some critical exponents. We also address the elusive regime α < 1 \\alpha < 1 , where we find that the universality class of both the ground-state and nonzero-temperature transition is consistent with the mean-field limit at α = 0 \\alpha = 0 . Our work not only contributes to the understanding of the equilibrium properties of long-range interacting quantum Ising models, but can also be important for addressing fundamental dynamical aspects, such as issues concerning the open question of thermalization in such models.