Thermodynamics and Universality for Mean Field Quantum Spin Glasses

Abstract

We study aspects of the thermodynamics of quantum versions of spin glasses. By means of the Lie-Trotter formula for exponential sums of operators, we adapt methods used to analyze classical spin glass models to answer analogous questions about quantum models.

17 pages

References in corpus (16)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Thermodynamic Limit in Mean Field Spin Glass Models
• An Extended Variational Principle for the SK Spin-Glass Model
• Mean-Field Theory of a Quantum Heisenberg Spin Glass
• Geometric Aspects of Quantum Spin States
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• Quantum Griffiths Singularities in the Transverse-Field Ising Spin Glass
• The Quantum Spherical p-Spin-Glass Model
• Free energy in the generalized Sherrington-Kirkpatrick mean field model
• The infinite volume limit in generalized mean field disordered models
• Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses?
• Nonrealistic Behavior of Mean Field Spin Glasses
• Quantum critical effects in mean-field glassy systems
• Thermodynamic Limit for Finite Dimensional Classical and Quantum Disordered Systems
• Structural Properties of the Disordered Spherical and other Mean Field Spin Models

Cited by in corpus (20)

• Existence of replica-symmetry breaking in quantum glasses
• Phase Diagram of the Quantum Random Energy Model
• Spectral Analysis of the Quantum Random Energy Model
• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses
• Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder
• Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams
• General properties of overlap operators in disordered quantum spin systems
• Bounds on the ground state energy of quantum $p$-spin Hamiltonians
• The Quantum Random Energy Model as a Limit of p-Spin Interactions
• Approach to equilibrium for a class of random quantum models of infinite range
• Self-averaging of perturbation Hamiltonian density in perturbed spin systems
• Absence of replica symmetry breaking in the transverse and longitudinal random field Ising model
• Some Observations for Mean-Field Spin Glass Models
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• The free energy of a quantum Sherrington-Kirkpatrick spin-glass model for weak disorder
• Zero-variance of perturbation Hamiltonian density in perturbed spin systems
• Universality of replica-symmetry breaking in the transverse field Sherrington-Kirkpatrick model
• Gauge theory for quantum XYZ spin glasses
• Free Energy Subadditivity for Symmetric Random Hamiltonians
• Trotter error and gate complexity of the SYK and sparse SYK models