Quantum TAP equations

Abstract

We derive Thouless-Anderson-Palmer (TAP) equations for quantum disordered systems. We apply them to the study of the paramagnetic and glassy phases in the quantum version of the spherical p spin-glass model. We generalize several useful quantities (complexity, threshold level, etc.) and various ideas (configurational entropy crisis, etc), that have been developed within the classical TAP approach, to quantum systems. The analysis of the quantum TAP equations allows us to show that the phase diagram (temperature-quantum parameter) of the p spin-glass model should be generic. In particular, we argue that a crossover from a second order thermodynamic transition close to the classical critical point to a first order thermodynamic transition close to the quantum critical point is to be expected in a large class of systems.

29 pages, 4 fig

References in corpus (5)

• The Quantum Spherical p-Spin-Glass Model
• Dynamics and transport in random quantum systems governed by strong-randomness fixed points
• From second to first order transitions in a disordered quantum magnet
• Time reparametrization group and the long time behaviour in quantum glassy systems
• Zero-temperature TAP equations for the Ghatak-Sherrington model

Cited by in corpus (45)

• The effective temperature
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Simple Glass Models and their Quantum Annealing
• First-order transitions and the performance of quantum algorithms in random optimization problems
• The Quantum Spherical p-Spin-Glass Model
• On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
• On quantum mean-field models and their quantum annealing
• Theory of the superglass phase
• Dissipative effects on quantum glassy systems
• Theory and simulations of quantum glass forming liquids
• Aging dynamics of quantum spin glasses of rotors
• Out of equilibrium dynamics of a Quantum Heisenberg Spin Glass
• Collective excitations and marginal stability of quantum Ising spin glasses
• A solvable model of quantum random optimization problems
• The quantum Biroli-Mézard model: glass transition and superfluidity in a quantum lattice glass model
• Effects of dissipation on disordered quantum spin models
• Dynamics of Disordered Quantum Systems Using Flow Equations
• Spectral Form Factor of a Quantum Spin Glass
• A Dynamical Study of the Quantum p=2 Spherical Model
• Quantum quenches in isolated quantum glasses out of equilibrium
• Mean field theory of superglasses
• Role of the Tracy-Widom distribution in the finite-size fluctuations of the critical temperature of the Sherrington-Kirkpatrick spin glass
• Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron
• A supersymmetric SYK model with a curious low energy behavior
• Thermal, quantum and simulated quantum annealing: analytical comparisons for simple models
• Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly non-ideal Bose gas
• Near-power-law temperature dependence of the superfluid stiffness in strongly disordered superconductors
• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Message-passing algorithm of quantum annealing with nonstoquastic Hamiltonian
• Role of initial conditions in the dynamics of quantum glassy systems
• A tentative replica theory of glassy Helium 4
• Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass
• The effect of quantum fluctuations on the coloring of random graphs
• Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
• Large time effective kinetics $\beta$-functions for quantum (2+p)-spin glass
• The quantum $p$-spin glass model: A user manual for holographers
• Slow nonequilibrium dynamics: parallels between classical and quantum glasses and gently driven systems
• Coarsening of Disordered Quantum Rotors under a Bias Voltage
• Dissipative quantum disordered models
• Information scrambling and butterfly velocity in quantum spin glass chains
• Time-translation invariance symmetry breaking hidden by finite-scale singularities
• Correspondence between excited energy eigenstates and local minima of energy landscape in quantum spin systems
• A p-Spin Interaction Ashkin-Teller Spin-Glass Model
• The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group