Quantum phase transitions

Abstract

In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behavior of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions are boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed on bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview over a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.

50 pages, 7 figs; (v2) final version as published

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• Superconducting charge-ordered states in cuprates
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• Fractional charges in pyrochlore lattices
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• Pinning of dynamic spin density wave fluctuations in the cuprate superconductors
• Charge Stripes and Antiferromagnetism in Insulating Nickelates and Superconducting Cuprates
• Chiral Symmetry Breaking in Abelian-Projected SU(2) Lattice Gauge Theory
• Multi-critical point in a diluted bilayer Heisenberg quantum antiferromagnet
• Projected SO(5) Models
• Long-range order versus random-singlet phases in quantum antiferromagnetic systems with quenched disorder
• Local field theory for disordered itinerant quantum ferromagnets
• Nature of the Quantum Phase Transition in Clean, Itinerant Heisenberg Ferromagnets
• Quantum vs. Geometric Disorder in a Two-Dimensional Heisenberg Antiferromagnet
• Quantum phase transitions in cuprates: stripes and antiferromagnetic supersolids
• Single-particle properties of a model for coexisting charge and spin quasi-critical fluctuations coupled to electrons
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• Local versus Nonlocal Order Parameter Field Theories for Quantum Phase Transitions
• Multichannel pseudogap Kondo model: Large-N solution and quantum-critical dynamics
• Definition of Magnetic Monopole Numbers for SU(N) Lattice Gauge-Higgs Models
• The pseudogap Fermi-Bose Kondo model
• The Critical Hopping Parameter in O(a) improved Lattice QCD
• Influence of rare regions on magnetic quantum phase transitions
• Some remarks about pseudo gap behavior of nearly antiferromagnetic metals

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• Adiabatic freezing of entanglement with insertion of defects in a one-dimensional Hubbard model
• Fidelity, Rosen-Zener Dynamics, Entropy and Decoherence in one dimensional hard-core bosonic systems
• Divergence of the Grüneisen ratio at symmetry-enhanced first-order quantum phase transitions
• Magnetic Grueneisen ratio of the random transverse-field Ising chain
• Zero temperature phase diagram of a d-wave superconductor with Anderson impurities
• Inducing critical phenomena in spin chains through sparse alternating fields
• A new strategy for directly calculating the minimum eigenvector of matrices without diagonalization
• Large time effective kinetics $\beta$-functions for quantum (2+p)-spin glass
• Quantum phase transitions: The mean-field perspective
• Quantum phase transition driven by competing intralayer and interlayer hopping in bilayer nickelates
• Hall coefficient in heavy fermion metals
• Phase diagram of a d-wave superconductor with Anderson impurities
• Conformal symmetry in quasi-free Markovian open quantum systems
• Learning Equivariant Maps with Variational Quantum Circuits
• Quantum Phase Transitions in periodically quenched systems
• Holographic duality and applications
• Driven-Dissipative Bose-Einstein Condensation and the Upper Critical Dimension
• Emergent soft-gap Anderson models at quantum criticality in a lattice Hamiltonian within dynamical mean field theory
• Quantum Phases and Spin Liquid Properties of 1T-TaS2
• Universal behavior of $\mathrm{CeP}{\mathrm{d}}_{1-\mathrm{x}}\mathrm{R}{\mathrm{h}}_{\mathrm{x}}$ Ferromagnet at Quantum Critical Point
• Peculiarity of the ${}^{12}$C$(0^{+})$ and ${}^{12}$C$(2^{+})$ energy spectrum in a 3$\alpha$ model
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
• Single-shot determination of quantum phases via continuous measurements
• Quantum phase transitions and ground-state correlations in BCS-like models
• Establishing simple relationship between eigenvector and matrix elements
• Resonator induced quantum phase transitions in a hybrid Josephson junction
• Zero Curvature Condition for Quantum Criticality
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Fisher Hartwig determinants, conformal field theory and universality in generalised XX models
• A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem
• Probing Hidden Symmetry and Altermagnetism with Sub-Picometer Sensitivity via Nonlinear Transport
• Transport anomalies in multiband superconductors near quantum critical point
• Interlayer Coupling-Induced Quantum Phase Transition in Quantum Anomalous Hall Multilayers
• Investigating Lipkin-Meshkov-Glick Model and Criticality-Enhanced Metrology in a Coherent Ising Machine
• Nonrelativistic Limit of Dirac Theory From Effective Field Theory
• Resolving mean-field solutions of dissipative phase transitions using permutational symmetry
• 3$d$ - 4$d$ hybridization anomaly in Ni${}_x$Pd${}_{1-x}$ alloys at quantum critical point
• Imaginary-time Quantum Relaxation Critical Dynamics with Semi-ordered Initial States
• Structure and scaling of Kitaev chain across a quantum critical point in real space
• Intertwined quantum phase transitions in the zirconium and niobium isotopes
• Ta2Pd3Te5 topological thermometer
• Holographic mean field theory and Kondo lattice
• Bound energy, entanglement and identifying critical points in 1D long-range Kitaev model
• Low energy properties of non-perturbative quantum systems: a space reduction approach
• Quantum jumps in amplitude bistability: Tracking a coherent and invertible state localization
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Temperature dependent energy gap for Yu-Shiba-Rusinov states at the quantum phase transition
• Computing quantum phase transitions
• Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench
• On the criticality of the configuration-space statistical geometry
• Persistence of charge density wave fluctuations in the absence of long-range order in a hole-doped kagome metal
• Julia Set in Quantum Evolution: The case of Dynamical Quantum Phase Transitions
• Thermodynamic properties of the field-induced Neel order of TlCuCl3
• Quantum Entanglement Control in Two-Spin-1/2 NMR Systems Through Magnetic Fields and Temperature
• Nexus between quantum criticality and the chemical potential pinning in high-$T_c$ cuprates
• Quantum Phase Transitions in Spin-1/2 Ising Chain in Regularly Alternating Transverse Field: Spin Correlation Functions
• Universal Mott quantum criticality in a modified periodic Anderson model
• Multipartite entanglement in quantum phase transitions
• Reaching Quantum Critical Point by Adding Non-magnetic Disorder in Single Crystals of Superconductor $({\text{Ca}}_x{\text{Sr}}_{1-x}{)}_3{\text{Rh}}_4{\text{Sn}}_{13}$
• Extended Bose-Hubbard Model on Small Grids: Exact Diagonalization and Monte Carlo Studies
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
• Tuning of superconducting properties with disorder in NbxSn nanocrystalline thin films
• On the application of Jucys-Murphy operators in the Hubbard model
• Designing non-equilibrium states of quantum matter through stochastic resetting
• Tilt-Induced Localization in Interacting Bose-Einstein Condensates for Quantum Sensing
• Quantum phase classification via partial tomography-based quantum hypothesis testing
• Two-dimensional transverse-field $XY$ model with the in-plane anisotropy and Dzyaloshinskii-Moriya interaction: Anisotropy-driven transition
• Quantum phase transitions in the multiphoton Jaynes-Cummings-Hubbard model
• Rectification from band gap oscillation
• On non-canonical degrees of freedom
• Absence of a dissipative quantum phase transition in Josephson junctions: Theory
• Supersymmetric Quantum Spherical Spins
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals
• Supersymmetric Quantum Spherical Spins with Short-Range Interactions
• Quantum Phase Transition in $\mathrm{CeCoI}{\mathrm{n}}_5$: Experimental Facts and Theory
• Marginal Fermi liquids from Fermi surfaces coupled via matrix boson gas
• Survival of Hermitian Criticality in the Non-Hermitian Framework
• Quantum critical behavior of diluted quasi-one-dimensional Ising chains
• Quantum Phase Recognition via Quantum Attention Mechanism