A field theory representation of sum of powers of principal minors and physical applications

• URL: http://arxiv.org/abs/2403.09874v1
• Date: Thu, 14 Mar 2024 21:09:46 GMT
• Title: A field theory representation of sum of powers of principal minors and physical applications
• Authors: M. N. Najafi, A. Ramezanpour, M. A. Rajabpour,
• Abstract summary: We introduce a novel field theory representation for the Sum of Powers of Principal Minors (SPPM) It offers deeper insights into the symmetries of complex quantum systems. This work bridges theoretical gaps in understanding principal minors within quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel field theory representation for the Sum of Powers of Principal Minors (SPPM), a mathematical construct with profound implications in quantum mechanics and statistical physics. We begin by establishing a Berezin integral formulation of the SPPM problem, showcasing its versatility through various symmetries including $SU(n)$, its subgroups, and particle-hole symmetry. This representation not only facilitates new analytical approaches but also offers deeper insights into the symmetries of complex quantum systems. For instance, it enables the representation of the Hubbard model's partition function in terms of the SPPM problem. We further develop three mean field techniques to approximate SPPM, each providing unique perspectives and utilities: the first method focuses on the evolution of symmetries post-mean field approximation, the second, based on the bosonic representation, enhances our understanding of the stability of mean field results, and the third employs a variational approach to establish a lower bound for SPPM. These methods converge to identical consistency relations and values for SPPM, illustrating their robustness. The practical applications of our theoretical advancements are demonstrated through two compelling case studies. First, we exactly solve the SPPM problem for the Laplacian matrix of a chain, a symmetric tridiagonal matrix, allowing for precise benchmarking of mean-field theory results. Second, we present the first analytical calculation of the Shannon-R\'enyi entropy for the transverse field Ising chain, revealing critical insights into phase transitions and symmetry breaking in the ferromagnetic phase. This work not only bridges theoretical gaps in understanding principal minors within quantum systems but also sets the stage for future explorations in more complex quantum and statistical physics models.

Related papers

• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics [4.1098478048719524]
  We propose an innovative framework based on nonequilibrium critical dynamics to preempt sign problem. By virtue of universal scaling theory of imaginary-time relaxation dynamics, we demonstrate that accurate critical point and critical exponents can be obtained in the short-time stage. We for the first time reveal the quantum phase diagram in the Hubbard model hosting $rm SU(3)$-symmetric Dirac fermions.
  arXiv  Detail & Related papers  (2024-10-24T15:37:45Z)
• Duality between string and computational order in symmetry-enriched topological phases [0.0]
  We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. We show that ground states of the toric code in an anisotropic magnetic field yield a natural, albeit non-computationally-universal, application of our framework.
  arXiv  Detail & Related papers  (2024-10-03T17:38:03Z)
• Simulating a quasiparticle on a quantum device [0.0]
  We propose a variational approach to explore quasiparticle excitations in interacting quantum many-body systems. We benchmark the proposed algorithm via numerical simulations performed on the one-dimension transverse field Ising chain. We show that the localized quasiparticle states constructed with VQE contain accessible information on the full band of quasiparticles.
  arXiv  Detail & Related papers  (2024-09-13T05:39:13Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• 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)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Experimental validation of the Kibble-Zurek Mechanism on a Digital Quantum Computer [62.997667081978825]
  The Kibble-Zurek mechanism captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. We experimentally tested the KZM for the simplest quantum case, a single qubit under the Landau-Zener evolution. We report on extensive IBM-Q experiments on individual qubits embedded in different circuit environments and topologies.
  arXiv  Detail & Related papers  (2022-08-01T18:00:02Z)
• Noncommutative polynomial optimization under symmetry [0.0]
  We present a general framework to exploit the symmetries present in the Navascu'es-Pironio-Ac'in semidefinite relaxations. We put equal emphasis on the moment and sum-of-squares dual approaches.
  arXiv  Detail & Related papers  (2021-12-20T19:02:16Z)
• Analytical nonadiabatic couplings and gradients within the state-averaged orbital-optimized variational quantum eigensolver [0.0]
  We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm. Motivated by the limitations of current quantum computers, the first extension consists in an efficient state-resolution procedure to find the SA-OO-VQE eigenstates. The second extension allows for the estimation of analytical gradients and non-adiabatic couplings.
  arXiv  Detail & Related papers  (2021-09-09T22:38:56Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)

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.