Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics

• URL: http://arxiv.org/abs/2303.16551v2
• Date: Fri, 5 Apr 2024 09:46:47 GMT
• Title: Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Authors: J. Khalouf-Rivera, Qian Wang, Lea F. Santos, J. E. García Ramos, M. Carvajal, F. Pérez-Bernal,
• Abstract summary: We analyze the degeneracy dependence on the size of two-level boson models with a $u(n+1)$ dynamical algebra. We show that the infinite-time average of out-of-time-order correlators is an ESQPT order parameter in finite systems with $n=1$, but in systems with $n>1$, this average only works as an order parameter in the mean-field limit.
• Score: 5.117091825006161
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Excited-state quantum phase transitions (ESQPTs) strongly influence the spectral properties of collective many-body quantum systems, changing degeneracy patterns in different quantum phases. Level degeneracies, in turn, affect the system's dynamics. We analyze the degeneracy dependence on the size of two-level boson models with a $u(n+1)$ dynamical algebra, where $n$ is the number of collective degrees of freedom. Below the ESQPT critical energy of these models, the energy gap between neighboring levels that belong to different symmetry sectors gets close to zero as the system size increases. We report and explain why this gap goes to zero exponentially for systems with one collective degree of freedom, but algebraically in models with more than one degree of freedom. As a consequence, we show that the infinite-time average of out-of-time-order correlators is an ESQPT order parameter in finite systems with $n=1$, but in systems with $n>1$, this average only works as an order parameter in the mean-field limit.

Related papers

• Observing super-quantum correlations across the exceptional point in a single, two-level trapped ion [48.7576911714538]
  In two-level quantum systems - qubits - unitary dynamics theoretically limit these quantum correlations to $2qrt2$ or 1.5 respectively. Here, using a dissipative, trapped $40$Ca$+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics.
  arXiv  Detail & Related papers  (2023-04-24T19:44:41Z)
• Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
  We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom. We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
  arXiv  Detail & Related papers  (2023-03-13T13:06:40Z)
• 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)
• Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models [4.965221313169878]
  We generalize the area-law violating models of Fredkin and Motzkin spin chains into two dimensions. The Hamiltonian is frustration free, and its projectors generate ergodic dynamics within the subspace of height configuration that are non negative.
  arXiv  Detail & Related papers  (2022-10-06T16:46:05Z)
• Anatomy of Dynamical Quantum Phase Transitions [0.0]
  We study periodic dynamical quantum phase transitions (DQPTs) directly connected to the zeros of a Landau order parameter (OP) We find that a DQPT signals a change in the dominant contribution to the wave function in the degenerate initial-state manifold. Our work generalizes previous results and reveals that, in general, periodic DQPTs comprise complex many-body dynamics fundamentally beyond that of two-level systems.
  arXiv  Detail & Related papers  (2022-10-05T18:00:00Z)
• 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)
• Dynamical quantum phase transitions in spin-$S$ $\mathrm{U}(1)$ quantum link models [0.0]
  Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body systems. We use infinite matrix product state techniques to study DQPTs in spin-$S$ $mathrmU(1)$ quantum link models. Our findings indicate that DQPTs are fundamentally different between the Wilson--Kogut--Susskind limit and its representation through the quantum link formalism.
  arXiv  Detail & Related papers  (2022-03-02T19:00:02Z)
• Quantum many-body spin rings coupled to ancillary spins: The sunburst quantum Ising model [0.0]
  We study a quantum "sunburst model" composed of a quantum Ising spin-ring in a transverse field. We observe rapid and nonanalytic changes in proximity of the quantum transitions of the Ising ring.
  arXiv  Detail & Related papers  (2022-02-16T11:22:19Z)
• 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)
• Dissipative dynamics at first-order quantum transitions [0.0]
  This issue is studied within the paradigmatic one-dimensional quantum Ising model. We analyze the out-of-equilibrium dynamics arising from quenches of the Hamiltonian parameters. We observe a regime where the system develops a nontrivial dynamic scaling behavior.
  arXiv  Detail & Related papers  (2020-09-23T14:08:21Z)
• 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.