Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions

• URL: http://arxiv.org/abs/2310.11951v2
• Date: Sat, 31 Aug 2024 06:55:12 GMT
• Title: Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions
• Authors: Yumeng Zeng, Bozhen Zhou, Shu Chen,
• Abstract summary: We show that the occurrence of exact zeros of fidelity in finite-size systems can be applied to detect quantum phase transitions. Our work provides a practicable way to detect quantum phase transitions via the calculation of fidelity of finite-size systems.
• Score: 4.350531579293999
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The fidelity is widely used to detect quantum phase transitions, which is characterized by either a sharp change of fidelity or the divergence of fidelity susceptibility in the thermodynamical limit when the phase-driving parameter is across the transition point. In this work, we unveil that the occurrence of exact zeros of fidelity in finite-size systems can be applied to detect quantum phase transitions. In general, the fidelity $\mathcal{F}(\gamma,\tilde{\gamma})$ always approaches zero in the thermodynamical limit, due to the Anderson orthogonality catastrophe, no matter whether the parameters of two ground states ($\gamma$ and $\tilde{\gamma}$) are in the same phase or different phases, and this makes it difficult to distinguish whether an exact zero of fidelity exists by finite-size analysis. To overcome the influence of orthogonality catastrophe, we study finite-size systems with twist boundary conditions, which can be introduced by applying a magnetic flux, and demonstrate that exact zeros of fidelity can be always accessed by tuning the magnetic flux when $\gamma$ and $\tilde{\gamma}$ belong to different phases. On the other hand, no exact zero of fidelity can be observed if $\gamma$ and $\tilde{\gamma}$ are in the same phase. We demonstrate the applicability of our theoretical scheme by studying concrete examples, including the Su-Schrieffer-Heeger model, Creutz model and Haldane model. Our work provides a practicable way to detect quantum phase transitions via the calculation of fidelity of finite-size systems.

Related papers

• 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)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Noise-induced phase transitions in hybrid quantum circuits [3.625262223613696]
  In this work, we investigate the effects of quantum noises with size-dependent probabilities $q=p/Lalpha$ where $alpha$ represents the scaling exponent. We have identified a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements. This unified picture further deepens the understanding of the connection between entanglement behavior and the capacity of information protection.
  arXiv  Detail & Related papers  (2024-01-30T00:03:56Z)
• Entanglement phase transition due to reciprocity breaking without measurement or post-selection [59.63862802533879]
  EPT occurs for a system undergoing purely unitary evolution. We analytically derive the entanglement entropy out of and at the critical point for the $l=1$ and $l/N ll 1$ case.
  arXiv  Detail & Related papers  (2023-08-28T14:28:59Z)
• Signatures of a quantum phase transition on a single-mode bosonic model [0.0]
  Equilibrium phase transitions emerge from the microscopic behavior of many-body systems. They can be defined through the non-analytic behavior of thermodynamic potentials in the thermodynamic limit. Taking previous ideas to the extreme, we argue that such a limit can be defined even in non-extended systems.
  arXiv  Detail & Related papers  (2023-03-22T20:14:45Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems [1.2514666672776884]
  We study the realization of the dynamical singularity of the rate function for finite-size systems under the twist boundary condition. We show that exact zeros of the Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point.
  arXiv  Detail & Related papers  (2022-11-06T14:35:57Z)
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model [44.58985907089892]
  How the property of quantum many-body system especially the phase transition will be affected by the non-hermiticity remains unclear. We show that there is a continuous phase transition induced by the non-hermiticity in QCP. We observe that the order parameter and susceptibility display infinitely even for finite size system, since non-hermiticity endows universality many-body system with different singular behaviour from classical phase transition.
  arXiv  Detail & Related papers  (2022-09-22T01:11:28Z)
• Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems [1.4065231184502454]
  We study exact zeros of Loschmidt echo and quantum speed limit time in finite size systems. Our results illustrate that exact zeros of Loschmidt echo exist even in finite size quantum systems.
  arXiv  Detail & Related papers  (2021-07-06T16:14:07Z)
• 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)
• 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.