Quantum phase transitions in transverse field spin models: from statistical physics to quantum information

Abstract

We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of the spin-1/2 Ising and XY models in a transverse field. Beginning with an overview of quantum phase transitions, we introduce a number of model Hamiltonians. We provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies. We also discuss Kitaev models and some other exactly solvable spin systems. Studies of quantum phase transitions in the presence of quenched randomness and with frustrating interactions are presented in detail. We discuss novel phenomena like Griffiths-McCoy singularities. We then turn to more recent topics like information theoretic measures of the quantum phase transitions in these models such as concurrence, entanglement entropy, quantum discord and quantum fidelity. We then focus on non-equilibrium dynamics of a variety of transverse field systems across quantum critical points and lines. After mentioning rapid quenching studies, we dwell on slow dynamics and discuss the Kibble-Zurek scaling for the defect density following a quench across critical points and its modifications for quenching across critical lines, gapless regions and multicritical points. Topics like the role of different quenching schemes, local quenching, quenching of models with random interactions and quenching of a spin chain coupled to a heat bath are touched upon. The connection between non-equilibrium dynamics and quantum information theoretic measures is presented at some length. We indicate the connection between Kibble-Zurek scaling and adiabatic evolution of a state as well as the application of adiabatic dynamics as a tool of a quantum optimization technique known as quantum annealing. The final section is dedicated to a detailed discussion on recent experimental studies of transverse Ising-like systems.

106 pages, 38 figures; an expanded version has been published as a book (330 pages, 72 figures, 874 references) as A. Dutta, G. Aeppli, B. K. Chakrabarti, U. Divakaran, T. F. Rosenbaum and D. Sen, Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information (Cambridge University Press, Cambridge, 2015)

References in corpus (12)

• Nonequilibrium dynamics of closed interacting quantum systems
• Periodic steady state and interference in a periodically driven quantum system
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Quantum Quenches, Thermalization and Many-Body Localization
• Quantum quench dynamics of the sine-Gordon model in some solvable limits
• Bound states and E_8 symmetry effects in perturbed quantum Ising chains
• A Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration
• Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching
• Berry Phases and Quantum Phase Transitions
• Renormalization group flows and quantum phase transitions: fidelity versus entanglement
• Staying adiabatic with unknown energy gap
• Analysis of entropy of XY Spin Chain

Cited by in corpus (104)

• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Collapse and revival of quantum many-body scars via Floquet engineering
• Mixed state dynamical quantum phase transition and emergent topology
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Strong Disorder RG approach - a short review of recent developments
• Finite-range interacting Ising quantum magnets with Rydberg atoms in optical lattices - From Rydberg superatoms to crystallization
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• Critical Phenomena and Kibble-Zurek Scaling in the Long-Range Quantum Ising Chain
• Multivariable Optimization: Quantum Annealing & Computation
• Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
• Quantum Criticality of an Ising-like Spin-1/2 Antiferromagnetic Chain in Transverse Magnetic Field
• Computational Complexity in Electronic Structure
• Tuning the presence of dynamical phase transitions in a generalized $XY$ spin chain
• Universal finite-time thermodynamics of many-body quantum machines from Kibble-Zurek scaling
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Effects of interactions on periodically driven dynamically localized systems
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Simulating Quantum Spin Models using Rydberg-Excited Atomic Ensembles in Magnetic Microtrap Arrays
• Quantum Ising chains with boundary fields
• Effects of periodic kicking on dispersion and wave packet dynamics in graphene
• Dynamical Quantum Phase Transitions in Extended Transverse Ising Models
• Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model
• Quantum Kibble-Zurek physics in long-range transverse-field Ising models
• Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators
• Controlling quantum critical dynamics of isolated systems
• Experimental Observation of Quantum Many-Body Excitations of $E_8$ Symmetry in the Ising Chain Ferromagnet CoNb${}_2$O${}_6$
• Two-step gap opening across the quantum critical point in a Kitaev honeycomb magnet
• Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential
• Dissipative polarization domain walls in a passive driven Kerr resonator
• Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field
• Measuring effective temperatures in a generalized Gibbs ensemble
• Dynamics of decoherence: universal scaling of the decoherence factor
• Phases and dynamics of ultracold bosons in a tilted optical lattice
• Quantum annealing and non-equilibrium dynamics of Floquet Chern insulators
• Signatures and conditions for phase band crossings in periodically driven integrable systems
• Steady states of a quasiperiodically driven integrable system
• Universal driven critical dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates
• Long-range random transverse-field Ising model in three dimensions
• Detecting out-of-time-order correlations via quasi-adiabatic echoes as a tool to reveal quantum coherence in equilibrium quantum phase transitions
• Excited-state quantum phase transition and the quantum speed limit
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath
• Quantum annealing speedup over simulated annealing on random Ising chains
• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Fibonacci steady states in a driven integrable quantum system
• Periodically driven Rydberg chains with staggered detuning
• Out-of-Time-Order correlators in driven conformal field theories
• Static and dynamical quantum correlations in phases of an alternating field XY model
• Quantum Phase Transitions detected by a local probe using Time Correlations and Violations of Leggett-Garg Inequalities
• Out of equilibrium dynamics of classical and quantum complex systems
• Effects of local periodic driving on transport and generation of bound states
• Emergence of string-valence bond solid state in the frustrated $J_1-J_2$ transverse field Ising model on the square lattice
• The Kitaev-Ising model, Transition between topological and ferromagnetic order
• Signatures of multifractality in a periodically driven interacting Aubry-André model
• Photo-induced Entanglement in a Magnonic Floquet Topological Insulator
• Dynamical Transition for a class of integrable models coupled to a bath
• Certified variational quantum algorithms for eigenstate preparation
• Quenching Dynamics and Quantum Information
• Dynamics of the quantum search and quench-induced first-order phase transitions
• Stroboscopic aliasing in long-range interacting quantum systems
• Single-ion properties of the transverse-field Ising model material CoNb${}_2$O${}_6$
• Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach
• Scale-invariant freezing of entanglement
• The A-Cycle Problem In XY model with Ring Frustration
• Josephson Ladders as a Model System for 1D Quantum Phase Transitions
• Exact results in Floquet coin toss for driven integrable models
• String and conventional order parameters in the solvable modulated quantum chain
• Numerical hardware-efficient variational quantum simulation of a soliton solution
• Partially disordered antiferromagnetism and multiferroic behavior in a frustrated Ising system, CoCl${}_2$-2SC(NH${}_2$)${}_2$
• Quantum Hysteresis in Coupled Light-Matter Systems
• The fate of current, residual energy and entanglement entropy in aperiodic driving of one dimensional Jordan Wigner integrable models
• Scaling in driven dynamics starting in the vicinity of a quantum critical point
• Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term
• Quantum fidelity approach to the ground state properties of the 1D ANNNI model in a transverse field
• Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain
• Solving Rubik's Cube via Quantum Mechanics and Deep Reinforcement Learning
• Entanglement scaling and spatial correlations of the transverse field Ising model with perturbations
• Random matrix theory and critical phenomena in quantum spin chains
• Quantum Phases of Yang-Mills Matrix Model Coupled to Fundamental Fermions
• Generation of concurrence between two qubits locally coupled to a one dimensional spin chain
• Effectof biquadratic exchange on the phase diagram of a spin-1 transverse XY modelwith single-ion anisotropy
• Low Temperature Domain Wall Freezing and Non-Equilibrium Dynamics in the Transverse-Field Ising Model Material CoNb${}_2$O${}_6$
• Quantum phase transition without gap opening
• Effect of double local quenches on Loschmidt echo and entanglement entropy of a one-dimensional quantum system
• Sudden quenches in quasiperiodic Ising model
• Quantum tricriticality in transverse Ising-like systems
• A quantum phase transition detected through one dimensional ballistic conductance
• The Quantum Geometric Tensor in a Parameter Dependent Curved Space
• Floquet engineering of edge states in the presence of staggered potential and interactions
• Inducing critical phenomena in spin chains through sparse alternating fields
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Hierarchy of correlations for the Ising model in the Majorana representation
• Critical behavior of order parameter at the nonequilibrium phase transition of the Ising model
• Absence of small-world effects at the quantum level and stability of the quantum critical point
• Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better
• Resolving mean-field solutions of dissipative phase transitions using permutational symmetry
• The quantum XY chain with boundary fields: finite-size gap and phase behavior
• Time-dependent Real-space Renormalization-Group Approach: application to an adiabatic random quantum Ising model
• Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field
• Equilibrium and Nonequilibrium phase transitions in continuous symmetric classical magnets
• Magnetic lattices for ultracold atoms