Detecting Many-Body Scars from Fisher Zeros

• URL: http://arxiv.org/abs/2501.09478v1
• Date: Thu, 16 Jan 2025 11:30:21 GMT
• Title: Detecting Many-Body Scars from Fisher Zeros
• Authors: Yuchen Meng, Songtai Lv, Yang Liu, Zefan Tan, Erhai Zhao, Haiyuan Zou,
• Abstract summary: We introduce an alternative route to detect and diagnose QMBS based on Fisher zeros. For systems with scars, a continuous line of Fisher zeros will appear off the imaginary $beta$ axis and extend upward. It has the advantage of easily spotting the emergence of scars without exhaustively examining each individual quantum state.
• Score: 4.06170462962629
• License:
• Abstract: The far-from-equilibrium dynamics of interacting quantum systems still defy precise understanding. One example is the so-called quantum many-body scars (QMBSs), where a set of energy eigenstates evade thermalization to give rise to long-lived oscillations. Despite the success of viewing scars from the perspectives of symmetry, commutant algebra and quasiparticles, it remains a challenge to elucidate the mechanism underlying all QMBS and to distinguish them from other forms of ergodicity breaking. In this work, we introduce an alternative route to detect and diagnose QMBS based on Fisher zeros, i.e. the patterns of zeros of the analytically continued partition function $Z$ on the complex $\beta$ (inverse temperature) plane. For systems with scars, a continuous line of Fisher zeros will appear off the imaginary $\beta$ axis and extend upward, separating the $\beta$ plane into regions with distinctive thermalization behaviors. This conjecture is motivated from interpreting the complex $Z$ as the survival amplitude of the thermofield double state, and it is validated by analyzing two models with QMBS, the $\bar{P}X\bar{P}$ model and the Ising chain in external fields. These models also illustrate another scenario of ergodicity breaking, where lines of Fisher zeros repeatedly intersect the imaginary $\beta$ axis. This ``statistical mechanics" approach places QMBS within the same framework of thermal and dynamical phase transitions. It has the advantage of easily spotting the emergence of scars without exhaustively examining each individual quantum state.

Related papers

• Scar-induced imbalance in staggered Rydberg ladders [0.0]
  We study the kinematically-constrained model of Rydberg atoms on a two-leg ladder with staggered detuning. QMBS result in coherent many-body revivals and site-dependent magnetization dynamics for both N'eel and Rydberg vacuum initial states.
  arXiv  Detail & Related papers  (2024-11-04T19:00:02Z)
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  The interplay between symmetry and topological properties plays a very important role in modern physics. How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• Exact Fisher zeros and thermofield dynamics across a quantum critical point [4.06170462962629]
  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.
  arXiv  Detail & Related papers  (2024-06-27T08:22:43Z)
• Theory of robust quantum many-body scars in long-range interacting systems [0.0]
  Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems. We show that long-range interacting quantum spin systems generically host robust QMBS. Our theory unveils the stability mechanism of such QMBS for arbitrary system size.
  arXiv  Detail & Related papers  (2023-09-21T22:00:40Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Duality between open systems and closed bilayer systems, and thermofield double states as quantum many-body scars [49.1574468325115]
  We find a duality between open many-body systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. Under this duality, the identity operator on the open system side maps to the thermofield double state. We identify broad classes of many-body open systems with nontrivial explicit eigen operators $Q$ of the Lindbladian superoperator.
  arXiv  Detail & Related papers  (2023-04-06T15:38:53Z)
• Weak Ergodicity Breaking in the Schwinger Model [0.0]
  We study QMBS in spin-$S$ $mathrmU(1)$ quantum link models with staggered fermions. We find that QMBS persist at $S>1/2$, with the resonant scarring regime, which occurs for a zero-mass quench. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension.
  arXiv  Detail & Related papers  (2022-03-16T18:00:01Z)
• Quantum Many-Body Scars in Spin-1 Kitaev Chains [1.340610646365466]
  We study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. We find that the scarred state is stable for perturbations which obey $vertmathbbZ_krangle$, while it becomes unstable against Heisenberg-type perturbations.
  arXiv  Detail & Related papers  (2022-01-23T10:11:32Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)
• Exact many-body scars and their stability in constrained quantum chains [55.41644538483948]
  Quantum scars are non-thermal eigenstates characterized by low entanglement entropy. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size.
  arXiv  Detail & Related papers  (2020-11-16T19:05:50Z)
• Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
  Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
  arXiv  Detail & Related papers  (2020-10-13T15:50:49Z)

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.