Quantum Phase Transitions  

In General > s.a. critical phenomena; phase transitions; quantum tunneling; relation with classical mechanics; states in statistical mechanics.
* Idea: They occur at zero temperature and involve the appearance of long-range correlations; They take place at the "quantum critical" value of some other parameter such as pressure, composition or magnetic field strength, and are due not to thermal fluctuations but to the intricate structure of a strongly entangled ground state.
* Formalism: A quantum phase transition requires that at least one of the Kato's exceptional-point parameters becomes real.
* Dynamical quantum phase transitions: Phase transitions triggered by internal changes in a non-equilibrium quantum system as it evolves in time (as opposed to driven by external factors such as temperature); They manifest themselves in discontinuous behavior of the system at certain critical times.
@ General references: Sondhi et al RMP(97) [continuous]; Sachdev pw(99)apr; Lombardo et al PRD(00)hp/99 [order parameter]; Schofield pw(03)aug; Shopova & Uzunov PRP(03); Carteret qp/04 [and renormalization]; Continentino & Ferreira PhyA(04) [first-order]; Rezakhani et al PRA(10)-a1004 [geometry]; Mostame et al PRA(10) [and decoherence]; Kruse et al PhyA(10) [and the third law]; Werlang et al PRL(10)-a1006 [critical points and quantum discord]; Nogueira a1009-ln [field-theoretic methods]; Sachdev 11; Braun et al PNAS(15)-a1403 [dynamics and emergence of coherence].
@ Fidelity-metric approach: Gu IJMPB(10)-a0811 [pedagogical]; Scherer et al JPA(09)-a0907 [Lipkin-Meshkov-Glick model].
@ Geometrical methods: Spitkovsky & Weis a1703 [geometrical signature]; Carollo et al PRP(19)-a1911; Tan a2003 [geometric measures of non-classicality].
@ Other formalisms: Zanardi et al qp/07 [differential geometry and information framework]; Kruse et al a0809 [framework]; Altintas & Eryigit AP(12)-a1202 [correlation and nonlocality measures as indicators]; Osychenko a1301-PhD [Monte Carlo study]; Wang et al PRX(15) [Monte Carlo approach to computing fidelity susceptibility]; Jiménez & Reslen PLA(16)-a1602 [grand-canonical approach]; > s.a. types of metrics [information geometry].
@ Entanglement: Vidal et al PRL(03)qp/02; Vidal et al PRA(04)cm/03 [second-order], PRA(04)cm/03 [first-order]; Somma et al PRA(04)qp; Chen JPA(07)cm/06 [and scaling]; Anders & Vedral OSID(07)qp/06-proc [macroscopic]; Kopp et al AP(07) [non-analyticity]; Rulli & Sarandy PRA(10)-a0912 [infinite-order, characterization]; Brody et al PLA(10) [N spin-1/2 particles, phase transition at T = 0]; Mousolou et al PRA(13)-a1303 [measure of entanglement and geometric phase]; > s.a. ising model.
@ Dynamical quantum phase transitions: Heyl et al PRL(13) [proposal, for 1D transverse-field Ising model]; Fläschner et al nPhys(18)-a1608 [topological]; Heyl & Budich PRB(17)-a1705 [topological, for mixed states]; Zhang et al Nat(17)nov-a1708 [in a quantum simulator]; Heyl RPP(18)-a1709 [rev]; Jurcevic PRL(17).
@ Related topics: Hamma qp/06 [and Berry phases]; Schützhold JLTP(08)-a1004 [non-equilibrium phenomena and amplification of quantum fluctuations]; Reid Phy(15)jul [and quasiparticles]; > s.a. Detectors in Quantum Theory.

Specific Types and Systems > s.a. Anderson Localization; Dicke Model; many-particle quantum systems; Open Systems.
@ Spin systems: Biskup et al CMP(07); Pan et al qp/07 [finite periodic XX spin-1/2 chain]; Chang & Wang a0801 [XY model]; Morrison & Parkins JPB(08)-a0805 [dissipation-driven]; Hoyos & Vojta PRL(08) [dissipative Ising model, smeared transition]; Heshami & Raeisi a0909 [matrix product state approach, XXZ spin-1 chain]; Albash & Haas Phy(11) [quantum spin liquid]; Fagotti a1308 [dynamical phase transitions]; Bonetto & Mastropietro a1406 [interacting fermionic chain]; Mzaouali et al PLA(19)-a1901 [in phase space]; > s.a. ising model; quantum coupled-spin models.
@ Condensates: Mur-Petit PRA(09)-a0906 [spin-1 system in magnetic field]; Aasen et al a1709 [fermion condensation]; > s.a. bose-einstein condensates; Fermi-Einstein Condensation; types of dark energy.
@ Topological phases: Xu & Zhang PRB(18)-a1807 [tensor-network approach]; Gong et al PRX(18) + Bandres & Segev Phy(18) [in non-Hermitian systems].
@ Nuclei: Leviatan & Macek PLB(12) [order and chaos in an interacting-boson model]; Elhatisari et al PRL(16) [liquid-like phase vs clusters of α particles].
@ Other systems: Porras & Cirac PRL(04)qp, PRL(04)qp [trapped ions and lasers]; Dunning et al JSM(06)qp [finite systems]; Kargol et al RVMP(08) [quantum anharmonic crystals]; Garrahan & Lesanovsky PRL(10) + Andrieux Phy(10) [quantum jumps as phase transitions between different kinds of temporal dynamics]; Sandvik PRL(10) + Singh Phy(10); Sachdev & Keimer PT(11)feb-a1102 [quantum matter at 0 K]; Banchi et al PRE(14)-a1305 [dissipative, quantum information geometry]; Borisov et al IJTP(15)-a1412 [multiply-degenerate exceptional points]; Vidmar et al PRL(15) + Clark Phy(15) [dynamical quasicondensation in an expanding gas]; Bausch et al PNAS(18)-a1512 [size-driven transitions].
@ Semiclassical: Douçot & Simon JPA(98) [order from disorder].

In Field Theory > s.a. black-hole thermodynamics; gravitational collapse; QED [lattice]; singularities; supersymmetry [breaking].
* Standard Model: The Standard Model of particle physics predicts two phase transitions that are relevant for the evolution of the early universe; One is responsible for the spontaneous electroweak symmetry breaking, the other is related to the spontaneous chiral symmetry breaking and confinement, and created 98% of the visible mass in the universe; > s.a. Chiral Symmetry.
* Gauge theory: There is a phase transition between weak and strong couplings; Examples of three fundamentally different types of behavior are that QCD is in a confined phase at zero temperature, while the electroweak sector of the Standard Model combines Coulomb and Higgs phases.
@ Gauge theory: Miransky & Yamawaki PRD(97) [conformal]; Aharony et al ATMP(04)ht/03 [deconfinement and length scales]; Apolloni et al NPB(06) [2D-Yang-Mills, large-N]; Liu et al NPB(09) [3D U(1) gauge theory of matter fields]; Ogilvie JPA(12)-a1211 [rev]; > s.a. quantum gauge theories.
@ And defect formation: Rivers et al PLB(02)hp.
@ Quantum field theory: Gianinetti & Parola PLA(00) [approach]; Zinn-Justin PRP(01)ht/00 [φ43 renormalization]; Kleinert & Schulte-Frohlinde 01 [φ4]; Höfling et al PRB(02)cm [3D Gross-Neveu model]; Splittorff et al PRD(03) [non-zero T and chemical potential]; Volovik LNP(07)cm/06 [from momentum-space topology]; Continentino 17; > s.a. states in quantum field theory [semiclassicality].
@ Lattice field theory: Cheluvaraja JPA(00) [abelian gauge theory]; Sergeev TMP(04) [3D]; van Enter & Shlosman cm/05-conf [sigma models]; Zurek & Dorner PTRS(08)-a0807 [phase transition in space]; Ostilli a0905 [from infinite dilution in Fock space].
@ Finite-temperature QCD: Meyer-Ortmanns RMP(96); Meyer-Ortmanns & Reisz 06; Schaffner-Bielich PoS-a0709, et al PoS-a0903 [and compact stars]; Sagert et al PRL(09) [and core-collapse supernovae]; news physorg(11)jun [experimental study]; > s.a. QCD phenomenology.

In Astrophysics / Gravity / the Early Universe > s.a. cosmological constant; observational cosmology; inflation; quantum gravity.
* Idea: Phase transitions occur when broken symmetries are restored at high T; The electroweak phase transition, which endows various particles with masses, and the QCD phase transition, which gives rise to confinement of quarks and gluons within hadrons in the true QCD vacuum, took place presumably at around 10−11 s and between 10−5 and 10−4 s, respectively, or at temperatures of about 300 GeV and 150 MeV.
@ Reviews: Gleiser CP(98)hp; Hwang MPLA(03); Straumann ap/04-ln; Boyanovsky et al ARNPS(06)hp; Kibble PT(07)sep [and condensed matter]; Hindmarsh et al SciPost-a2008 [in the early universe, introduction].
@ General references: Coleman PRD(77), & Callan PRD(77); Linde RPP(79); Hiscock PRD(87) [and black holes]; Huang CQG(93)gq/04 [quantum field theory effects]; Goldman et al PLA(96) [galaxy-galaxy correlations]; Sigl et al PRD(97) [primordial B field]; Borghini et al JPG(00)hp [quark-hadron]; Gleiser & Trodden PLB(01) [and fermion production]; Fraga & Venugopalan PhyA(05) [first-order, finite-size effects]; Easther et al PRD(09)-a0907 [bubble nucleation from classical transitions]; Rakić et al PoS-a0912; Camanho et al PRD(12)-a1204 [bubble nucleation in anti-de Sitter space]; Giblin & Mertens JHEP(13)-a1310 [with order parameter coupled to a relativistic fluid].
@ QCD phase transition: Hwang IJMPA(08); Boeckel & Schaffner-Bielich PRL(10) [short period of inflation]; > s.a. early-universe baryogenesis; magnetism.
> Related topics: see sources of gravitational radiation; symmetry breaking; topological defects.

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