Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation

• URL: http://arxiv.org/abs/2305.10482v2
• Date: Fri, 20 Oct 2023 04:07:01 GMT
• Title: Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation
• Authors: Juan Rom\'an-Roche, V\'ictor Herr\'aiz-L\'opez, David Zueco
• Abstract summary: We present an exact analytical solution for quantum strong long-range models in the canonical ensemble. We utilize the equivalence between generalized Dicke models and interacting quantum models as a generalization of the Hubbard-Stratonovich transformation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an exact analytical solution for quantum strong long-range models in the canonical ensemble by extending the classical solution proposed in [Campa et al., J. Phys. A 36, 6897 (2003)]. Specifically, we utilize the equivalence between generalized Dicke models and interacting quantum models as a generalization of the Hubbard-Stratonovich transformation. To demonstrate our method, we apply it to the Ising chain in transverse field and discuss its potential application to other models, such as the Fermi-Hubbard model, combined short and long-range models and models with antiferromagnetic interactions. Our findings indicate that the critical behaviour of a model is independent of the range of interactions, within the strong long-range regime, and the dimensionality of the model. Moreover, we show that the order parameter expression is equivalent to that provided by mean-field theory, thus confirming the exactness of the latter. Finally, we examine the algebraic decay of correlations and characterize its dependence on the range of interactions in the full phase diagram.

Related papers

• Systematic compactification of the (multi) two-channel Kondo model. III. Extended field-theoretic renormalization group analysis [68.8204255655161]
  We calculate the detailed flow for the (multi) two-channel Kondo model and its compactified versions. We gain insights into the contradistinction between the consistent vs. conventional bosonization-debosonization formalisms.
  arXiv  Detail & Related papers  (2023-08-07T14:07:21Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• 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)
• New insights on the quantum-classical division in light of Collapse Models [63.942632088208505]
  We argue that the division between quantum and classical behaviors is analogous to the division of thermodynamic phases. A specific relationship between the collapse parameter $(lambda)$ and the collapse length scale ($r_C$) plays the role of the coexistence curve in usual thermodynamic phase diagrams.
  arXiv  Detail & Related papers  (2022-10-19T14:51:21Z)
• 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)
• Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions [0.0]
  The pattern obtained from the entanglement between any two arbitrary sites of the long-range model can be mimicked by the model having a finite range of interactions. We show that the monogamy score of entanglement is in good agreement with the behavior of pairwise entanglement.
  arXiv  Detail & Related papers  (2022-06-18T12:45:13Z)
• Topological correlations in three dimensional classical Ising models: an exact solution with a continuous phase transition [8.83889166043817]
  We study a 3D classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases.
  arXiv  Detail & Related papers  (2022-02-23T04:22:30Z)
• Entropy Production and the Role of Correlations in Quantum Brownian Motion [77.34726150561087]
  We perform a study on quantum entropy production, different kinds of correlations, and their interplay in the driven Caldeira-Leggett model of quantum Brownian motion.
  arXiv  Detail & Related papers  (2021-08-05T13:11:05Z)
• Emergent fractal phase in energy stratified random models [0.0]
  We study the effects of partial correlations in kinetic hopping terms of long-range random matrix models on their localization properties. We show that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system.
  arXiv  Detail & Related papers  (2021-06-07T18:00:01Z)
• Underlying SUSY in a generalized Jaynes-Cummings model [0.0]
  Our model features an underlying Lie graded algebra symmetry reminiscent to supersymmetric quantum mechanics. We show the evolution of the population inversion and the boson quadratures for an initial state.
  arXiv  Detail & Related papers  (2020-10-26T19:35:05Z)
• Dynamical hysteresis properties of the driven-dissipative Bose-Hubbard model with a Gutzwiller Monte Carlo approach [0.0]
  We study the dynamical properties of a driven-dissipative Bose-Hubbard model in the strongly interacting regime. We take classical and quantum correlations into account. We show that approximation techniques relying on a unimodal distribution such as the mean field and $1/z$ expansion drastically underestimate the particle number fluctuations.
  arXiv  Detail & Related papers  (2020-08-17T13:50:10Z)

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.