Comparison of finite-temperature topological indicators based on Uhlmann connection

• URL: http://arxiv.org/abs/2108.05016v1
• Date: Wed, 11 Aug 2021 04:02:00 GMT
• Title: Comparison of finite-temperature topological indicators based on Uhlmann connection
• Abstract summary: Two indicators of finite-temperature topological properties based on the Uhlmann connection are studied. The signature from the Uhlmann-Wilson loop gradually fades away as temperature increases. The Berry phase exhibits quantization due to the underlying holonomy group.
• Score: 6.632129400203799
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Two indicators of finite-temperature topological properties based on the Uhlmann connection, one generalizing the Wilson loop to the Uhlmann-Wilson loop and the other generalizing the Berry phase to the Uhlmann phase, are constructed explicitly for a time-reversal invariant topological insulators with a $Z_2$ index. While the phases of the eigenvalues of the Wilson loop reflect the $Z_2$ index of the model at zero temperature, it is found that the signature from the Uhlmann-Wilson loop gradually fades away as temperature increases. On the other hand, the Berry phase exhibits quantization due to the underlying holonomy group. The Uhlmann phase retains the quantization at finite temperatures and serves as an indicator of topological properties. A phase diagram showing where jumps of the Uhlmann phase can be found is presented. By modifying the model to allow higher winding numbers, finite-temperature topological regimes sandwiched between trivial regimes at high and low temperatures may emerge.

Related papers

• SYK thermal expectations are classically easy at any temperature [49.788604174558564]
  We give a simple classical algorithm that approximates thermal expectations.<n>We show it has quasi-polynomial cost $nO(log n/)$ for all temperatures above a phase transition in the free energy.
  arXiv  Detail & Related papers  (2026-02-26T04:48:32Z)
• Thermal Uhlmann-Chern Number: Bridging Pure and Mixed States [7.3022646129024595]
  We introduce the thermal Uhlmann-Chern number, a generalization of the Chern number, to characterize the topological properties of mixed states.<n>We provide a rigorous mathematical proof that the first- and higher-order Uhlmann-Chern numbers converge to the corresponding Chern numbers in the zero-temperature limit.<n>Our results establish a robust bridge between the topological properties of pure and mixed states, offering new insights into finite-temperature topological phases.
  arXiv  Detail & Related papers  (2025-06-22T13:03:25Z)
• Uhlmann and scalar Wilczek-Zee phases of degenerate quantum systems [6.303505475375988]
  The Wilczek-Zee holonomy arises in degenerate states while the Uhlmann holonomy characterizes finite-temperature topology.<n>We investigate possible relationships between the Uhlmann phase and the scalar WZ phase, which reflects the Uhlmann and WZ holonomy respectively.<n>Some conditions are derived in an analytic analysis, under which the Uhlmann phase in the zero-temperature limit converges to the scalar WZ phase.
  arXiv  Detail & Related papers  (2025-05-21T15:01:52Z)
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• Quantum chaos and thermalization in the two-mode Dicke model [77.34726150561087]
  We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model. The two-mode Dicke model exhibits normal to superradiant quantum phase transition. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size.
  arXiv  Detail & Related papers  (2022-07-08T11:16:29Z)
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model [77.34726150561087]
  We study the microscopic dynamics of competing ordered phases in a two-dimensional correlated electron model. We simulate the light-induced transition between two competing phases.
  arXiv  Detail & Related papers  (2022-05-13T13:13:31Z)
• Uhlmann holonomy against Lindblad dynamics of topological systems at finite temperatures [1.788349916009287]
  We test the Uhlmann holonomy against various system-environment couplings in quantum dynamics. The Uhlmann phase is shown to remain quantized in all the examples if the initial state is topological.
  arXiv  Detail & Related papers  (2022-05-11T17:40:07Z)
• Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing [58.720142291102135]
  We investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation.
  arXiv  Detail & Related papers  (2022-03-28T14:55:28Z)
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and $\mathrm{RP}^2$ models: zero-temperature phase transition versus finite-temperature crossover [0.0]
  We compare the two-dimensional classical Heisenberg and $mathrmRP2$ models. For the Heisenberg model, we find no signs of a finite-temperature phase transition. For the $mathrmRP2$ model, we observe an abrupt onset of scaling behaviour.
  arXiv  Detail & Related papers  (2022-02-15T17:35:15Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Probing the superfluid-insulator phase transition by a non-Hermitian external field [0.0]
  We study the response of a thermal state of the Hubbard-like system to either global or local non-Hermitian perturbations. We show that the dynamical response of the system is strongly sensitive to the underlying quantum phase transition (QPT) from a Mott insulator to a superfluid state.
  arXiv  Detail & Related papers  (2021-06-29T00:47:40Z)
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results [68.8204255655161]
  We show that the proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates.
  arXiv  Detail & Related papers  (2021-05-11T14:08:02Z)
• Finite-temperature topological phase transitions of spin-$j$ systems in Uhlmann processes: General formalism and experimental protocols [2.6514968639939296]
  We analyze an ideal spin-j quantum paramagnet in a magnetic field undergoing an Uhlmann process. A quantized jump of the Uhlmann phase signifies a topological quantum phase transition (TQPT) of the underlying process. The exact results of j=1/2 and j=1 systems show topological regimes that only survive at finite temperatures but not at zero temperature.
  arXiv  Detail & Related papers  (2021-03-29T05:10:58Z)
• Topological Uhlmann phase transitions for a spin-j particle in a magnetic field [0.0]
  The Uhlmann phase of such a system as the spin-$j particle in presence of a slowly rotating magnetic field has not been reported to date. We find that the Uhlmann phase is given by the argument of a complex second kind Chebyshev of order $2j$.
  arXiv  Detail & Related papers  (2021-02-26T23:01:00Z)

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.