Exact Fisher zeros and thermofield dynamics across a quantum critical point

• URL: http://arxiv.org/abs/2406.18981v3
• Date: Tue, 24 Sep 2024 15:17:19 GMT
• Title: Exact Fisher zeros and thermofield dynamics across a quantum critical point
• Authors: Yang Liu, Songtai Lv, Yuchen Meng, Zefan Tan, Erhai Zhao, Haiyuan Zou,
• Abstract summary: We show how Fisher zeros can be employed to better understand quantum phase transitions or the non-unitary dynamics of open quantum systems. We point out $Z$ can be realized and probed in monitored quantum circuits.
• Score: 4.06170462962629
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: By setting the inverse temperature $\beta$ loose to occupy the complex plane, Michael E. Fisher showed that the zeros of the complex partition function $Z$, if approaching the real $\beta$ axis, reveal a thermodynamic phase transition. More recently, Fisher zeros were used to mark the dynamical phase transition in quench dynamics. It remains unclear, however, how Fisher zeros can be employed to better understand quantum phase transitions or the non-unitary dynamics of open quantum systems. Here we answer this question by a comprehensive analysis of the analytically continued one-dimensional transverse field Ising model. We exhaust all the Fisher zeros to show that in the thermodynamic limit they congregate into a remarkably simple pattern in the form of continuous open or closed lines. These Fisher lines evolve smoothly as the coupling constant is tuned, and a qualitative change identifies the quantum critical point. By exploiting the connection between $Z$ and the thermofield double states, we obtain analytical expressions for the short- and long-time dynamics of the survival amplitude including its scaling behavior at the quantum critical point. We point out $Z$ can be realized and probed in monitored quantum circuits. The exact analytical results are corroborated by numerical tensor renormalization group. We further show similar patterns of Fisher zeros also emerge in other spin models. Therefore the approach outlined may serve as a powerful tool for interacting quantum systems.

Related papers

• Semiclassical Quantum Trajectories in the Monitored Lipkin-Meshkov-Glick Model [41.94295877935867]
  We investigate the dynamics of the Lipkin-Meshkov-Glick model, composed of $N$ all-to-all interacting spins $1/2$, under a weak external monitoring. We derive a set of semiclassical equations describing the evolution of the expectation values of global spin observables, which become exact in the thermodynamic limit. The transition is not affected by post-selection issues, as it is already visible at the level of ensemble averages.
  arXiv  Detail & Related papers  (2024-07-29T18:00:00Z)
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators [5.743814444071535]
  Parametrically driven nonlinear resonators represent building block for realizing fault-tolerant quantum computation. Critical phenomena can occur without interaction with any other quantum system. This work reveals that the quantum metric and Berry curvature display diverging behaviors across the quantum phase transition.
  arXiv  Detail & Related papers  (2023-12-22T03:31:58Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Scalable Spin Squeezing from Finite Temperature Easy-plane Magnetism [26.584014467399378]
  We conjecture that any Hamiltonian exhibiting finite temperature, easy-plane ferromagnetism can be used to generate scalable spin squeezing. Our results provide insights into the landscape of Hamiltonians that can be used to generate metrologically useful quantum states.
  arXiv  Detail & Related papers  (2023-01-23T18:59:59Z)
• Signatures of quantum criticality in the complex inverse temperature plane [7.628970142172651]
  We identify different Fisher zeros on lines or closed curves and elucidate their correspondence with domain-wall excitations or confined mesons for the one-dimensional transverse field Ising model. The crossover behavior of the Fisher zeros provides a fascinating picture for criticality near the quantum phase transition. Our results unambiguously show significant features of Fisher zeros for a quantum phase transition and open up a new route to explore quantum criticality.
  arXiv  Detail & Related papers  (2022-11-02T01:22:28Z)
• Multipartite Entanglement in Crossing the Quantum Critical Point [6.24959391399729]
  We investigate the multipartite entanglement for a slow quantum quench crossing a critical point. We consider the quantum Ising model and the Lipkin-Meshkov-Glick model, which are local and full-connected quantum systems, respectively.
  arXiv  Detail & Related papers  (2022-02-16T06:58:10Z)
• Quantum quench thermodynamics at high temperatures [0.0]
  entropy produced when a system undergoes an infinitesimal quench is directly linked to the work parameter susceptibility, making it sensitive to the existence of a quantum critical point. We show that these individual contributions continue to exhibit signatures of the quantum phase transition, even at arbitrarily high temperatures.
  arXiv  Detail & Related papers  (2021-09-08T15:20:50Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{PT}$ symmetry to quantum fluctuations [0.0]
  We study a minimal model that has a driven-dissipative quantum phase transition. We analyze the critical phenomena in this system, showing which aspects can be captured by each approach. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.
  arXiv  Detail & Related papers  (2020-07-02T22:39:35Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.