Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model

• URL: http://arxiv.org/abs/2105.11551v1
• Date: Mon, 24 May 2021 21:48:34 GMT
• Title: Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
• Authors: Daniel Guti\'errez-Ruiz, Diego Gonzalez, Jorge Ch\'avez-Carlos, Jorge G. Hirsch, and J. David Vergara
• Abstract summary: We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground state quantum phase transition, where a bifurcation occurs. For a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest energy state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground state quantum phase transition, where a bifurcation occurs, showing a change of stability associated with an excited state quantum phase transition. Symmetrically, for a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest energy state. Employing the Holstein-Primakoff approximation, we derive analytic expressions for the quantum metric tensor and compute the scalar and Berry curvatures. We contrast the analytic results with their finite-size counterparts obtained through exact numerical diagonalization and find an excellent agreement between them for large sizes of the system in a wide region of the parameter space, except in points near the phase transition where the Holstein-Primakoff approximation ceases to be valid.

Related papers

• Identifying non-Hermitian critical points with quantum metric [2.465888830794301]
  The geometric properties of quantum states are encoded by the quantum geometric tensor. For conventional Hermitian quantum systems, the quantum metric corresponds to the fidelity susceptibility. We extend this wisdom to the non-Hermitian systems for revealing non-Hermitian critical points.
  arXiv  Detail & Related papers  (2024-04-24T03:36:10Z)
• Probing quantum floating phases in Rydberg atom arrays [61.242961328078245]
  We experimentally observe the emergence of the quantum floating phase in 92 neutral-atom qubits. The site-resolved measurement reveals the formation of domain walls within the commensurate ordered phase. As the experimental system sizes increase, we show that the wave vectors approach a continuum of values incommensurate with the lattice.
  arXiv  Detail & Related papers  (2024-01-16T03:26:36Z)
• 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)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Characterizing quantum criticality and steered coherence in the XY-Gamma chain [0.37498611358320727]
  We analytically solve the one-dimensional short-range interacting case with the Jordan-Wigner transformation. In the gapless phase, an incommensurate spiral order is manifested by the vector-chiral correlations. We derive explicit scaling forms of the excitation gap near the quantum critical points.
  arXiv  Detail & Related papers  (2022-06-08T15:28:10Z)
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models [0.0]
  We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. We find that, in the thermodynamic limit, they have the same divergent behavior near the quantum phase transition. We also show that the scalar curvature is only defined on one of the system's phases and that it approaches a negative constant value.
  arXiv  Detail & Related papers  (2021-07-12T22:11:45Z)
• Fidelity susceptibility near topological phase transitions in quantum walks [0.0]
  We show that for topological phase transitions in Dirac models, the fidelity susceptibility coincides with the curvature function whose integration gives the topological invariant. We map out the profile and criticality of the fidelity susceptibility to quantum walks that simulate one-dimensional class BDI and two-dimensional class D Dirac models.
  arXiv  Detail & Related papers  (2020-07-21T09:11:52Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Classical, semiclassical and quantum signatures of quantum phase transitions in a (pseudo) relativistic many-body system [0.0]
  We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in bosonic gases. We numerically investigate the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.
  arXiv  Detail & Related papers  (2020-07-09T09:08:17Z)
• 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)
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics [68.8204255655161]
  We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process. We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
  arXiv  Detail & Related papers  (2020-01-13T14:30:36Z)

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.