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Title: Space and time renormalization in phase transition dynamics

Abstract

Here, when a system is driven across a quantum critical point at a constant rate, its evolution must become nonadiabatic as the relaxation time τ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length ξˆ set at the time tˆ=τˆ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigating an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.

Authors:
 [1];  [2];  [3];  [4]
  1. Instytut Fizyki Uniwersytetu Jagiellonskiego, Krakow (Poland); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Instytut Fizyki Uniwersytetu Jagiellonskiego, Krakow (Poland)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Silesia, Katowice (Poland)
  4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1255132
Alternate Identifier(s):
OSTI ID: 1238393
Report Number(s):
LA-UR-15-28631
Journal ID: ISSN 2469-9950; PRBMDO
Grant/Contract Number:  
DEC-2013/09/B/ST3/01603; AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 93; Journal Issue: 7; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Francuz, Anna, Dziarmaga, Jacek, Gardas, Bartłomiej, and Zurek, Wojciech H. Space and time renormalization in phase transition dynamics. United States: N. p., 2016. Web. doi:10.1103/PhysRevB.93.075134.
Francuz, Anna, Dziarmaga, Jacek, Gardas, Bartłomiej, & Zurek, Wojciech H. Space and time renormalization in phase transition dynamics. United States. https://doi.org/10.1103/PhysRevB.93.075134
Francuz, Anna, Dziarmaga, Jacek, Gardas, Bartłomiej, and Zurek, Wojciech H. 2016. "Space and time renormalization in phase transition dynamics". United States. https://doi.org/10.1103/PhysRevB.93.075134. https://www.osti.gov/servlets/purl/1255132.
@article{osti_1255132,
title = {Space and time renormalization in phase transition dynamics},
author = {Francuz, Anna and Dziarmaga, Jacek and Gardas, Bartłomiej and Zurek, Wojciech H.},
abstractNote = {Here, when a system is driven across a quantum critical point at a constant rate, its evolution must become nonadiabatic as the relaxation time τ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length ξˆ set at the time tˆ=τˆ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigating an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.},
doi = {10.1103/PhysRevB.93.075134},
url = {https://www.osti.gov/biblio/1255132}, journal = {Physical Review B},
issn = {2469-9950},
number = 7,
volume = 93,
place = {United States},
year = {Thu Feb 18 00:00:00 EST 2016},
month = {Thu Feb 18 00:00:00 EST 2016}
}

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Cited by: 56 works
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Works referenced in this record:

Emergence of coherence via transverse condensation in a uniform quasi-two-dimensional Bose gas
journal, January 2015


Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
journal, December 2008


Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model
journal, December 2005


Theory of defect production in nonlinear quench across a quantum critical point
journal, January 2009


Classical, quantum and total correlations
journal, August 2001


Kibble-Zurek mechanism in a quenched ferromagnetic Bose-Einstein condensate
journal, October 2007


Entropy and correlation functions of a driven quantum spin chain
journal, April 2006


The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
journal, February 1994


Colloquium : Nonequilibrium dynamics of closed interacting quantum systems
journal, August 2011


Nonlinear electric transport in graphene: Quantum quench dynamics and the Schwinger mechanism
journal, April 2010


Exploring Symmetry Breaking at the Dicke Quantum Phase Transition
journal, September 2011


Direct Observation of the Proliferation of Ferroelectric Loop Domains and Vortex-Antivortex Pairs
journal, April 2012


Phase-transition dynamics in the lab and the universe
journal, September 2007


Spontaneous vortices in the formation of Bose–Einstein condensates
journal, October 2008


Defect Production in Nonlinear Quench across a Quantum Critical Point
journal, July 2008


Quenching dynamics of a quantum X Y spin- 1 2 chain in a transverse field
journal, November 2007


Nonequilibrium Dynamic Critical Scaling of the Quantum Ising Chain
journal, July 2012


Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system
journal, February 2010


Vortex String Formation in a 3D U(1) Temperature Quench
journal, April 1999


Spontaneous creation of Kibble–Zurek solitons in a Bose–Einstein condensate
journal, September 2013


Defect production due to quenching through a multicritical point
journal, February 2009


Universal adiabatic dynamics in the vicinity of a quantum critical point
journal, October 2005


Cosmological experiments in superfluid helium?
journal, October 1985


Vortex Formation in Two Dimensions: When Symmetry Breaks, How Big Are the Pieces?
journal, June 1998


Spontaneous nucleation and dynamics of kink defects in zigzag arrays of trapped ions
journal, May 2013


Scaling of ground-state fidelity in the thermodynamic limit: X Y model and beyond
journal, September 2011


Topological defects as relics of emergent continuous symmetry and Higgs condensation of disorder in ferroelectrics
journal, November 2014


Quench dynamics and defect production in the Kitaev and extended Kitaev models
journal, July 2008


Dynamics of a quantum phase transition and relaxation to a steady state
journal, September 2010


Density of Kinks after a Quench: When Symmetry Breaks, How Big are the Pieces?
journal, March 1997


Statistical Mechanics of the X Y Model. II. Spin-Correlation Functions
journal, February 1971


Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate
journal, September 2006


Topology of cosmic domains and strings
journal, August 1976


Quantum phase transition in space in a ferromagnetic spin-1 Bose–Einstein condensate
journal, June 2009


Spontaneous fluxoid formation in superconducting loops
journal, November 2009


Vortex formation in neutron-irradiated superfluid 3He as an analogue of cosmological defect formation
journal, July 1996


Symmetry Breaking with a Slant: Topological Defects after an Inhomogeneous Quench
journal, June 1999


Universal far-from-equilibrium dynamics of a holographic superconductor
journal, June 2015


Ginzburg regime and its effects on topological defect formation
journal, August 2000


Some implications of a cosmological phase transition
journal, December 1980


Critical dynamics of decoherence
journal, June 2011


Observation of Magnetic Flux Generated Spontaneously During a Rapid Quench of Superconducting Films
journal, November 2003


Quantum Discord: A Measure of the Quantumness of Correlations
journal, December 2001


Kibble-Zurek problem: Universality and the scaling limit
journal, August 2012


Cosmological experiments in condensed matter systems
journal, November 1996


Trapping of Topological-Structural Defects in Coulomb Crystals
journal, March 2013


Cooling dynamics of pure and random Ising chains
journal, March 2009


Formation of helical ion chains
journal, January 2016


Quench-Induced Supercurrents in an Annular Bose Gas
journal, September 2014


Adiabatic dynamics in passage across quantum critical lines and gapless phases
journal, January 2010


Dynamics of an inhomogeneous quantum phase transition
journal, May 2010


Defect Formation beyond Kibble-Zurek Mechanism and Holography
journal, May 2015


Dynamics of Quantum Phase Transition in an Array of Josephson Junctions
journal, April 2002


Universality of phase transition dynamics: Topological defects from symmetry breaking
journal, March 2014


Exact Results for Quench Dynamics and Defect Production in a Two-Dimensional Model
journal, February 2008


Kibble–Zurek scaling and string-net coarsening in topologically ordered systems
journal, September 2013


Scaling Behavior and Beyond Equilibrium in the Hexagonal Manganites
journal, December 2012


Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
journal, September 2013


Winding up superfluid in a torus via Bose Einstein condensation
journal, April 2012


Causality in Condensates: Gray Solitons as Relics of BEC Formation
journal, March 2009


Reverse quenching in a one-dimensional Kitaev model
journal, June 2009


Quantum Quench of an Atomic Mott Insulator
journal, June 2011


Optimal Nonlinear Passage Through a Quantum Critical Point
journal, August 2008


Quenching along a gapless line: A different exponent for defect density
journal, October 2008


Observation of Spontaneous Flux Generation in a Multi-Josephson-Junction Loop
journal, May 2000


Dynamics of a Quantum Phase Transition
journal, September 2005


Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas
journal, January 2015


Solitons as the Early Stage of Quasicondensate Formation during Evaporative Cooling
journal, March 2011


Spontaneous nucleation of structural defects in inhomogeneous ion chains
journal, November 2010


Entanglement in Quantum Critical Phenomena
journal, June 2003


Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals
journal, August 2013


Observation of the Kibble–Zurek scaling law for defect formation in ion crystals
journal, August 2013


Winding Up of the Wave-Function Phase by an Insulator-to-Superfluid Transition in a Ring of Coupled Bose-Einstein Condensates
journal, September 2008


Structural Defects in Ion Chains by Quenching the External Potential: The Inhomogeneous Kibble-Zurek Mechanism
journal, August 2010


Effects of interference in the dynamics of a spin- 1/2 transverse XY chain driven periodically through quantum critical points
journal, May 2009


Laboratory simulation of cosmic string formation in the early Universe using superfluid 3He
journal, July 1996


Defect generation in a spin- 1 2 transverse X Y chain under repeated quenching of the transverse field
journal, June 2008


Scaling of the entanglement spectrum in driven critical dynamics
journal, May 2015


Cosmology in the Laboratory: Defect Dynamics in Liquid Crystals
journal, March 1991


Soliton Creation During a Bose-Einstein Condensation
journal, April 2010


Dynamics of the entanglement spectrum in spin chains
journal, June 2014


Emergence of coherence and the dynamics of quantum phase transitions
journal, March 2015


Works referencing / citing this record:

Exploring the Kibble–Zurek mechanism with homogeneous Bose gases
journal, January 2017


Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians
journal, October 2018


Universality of miscible–immiscible phase separation dynamics in two-component Bose–Einstein condensates
journal, February 2019


Dynamics of longitudinal magnetization in transverse-field quantum Ising model: from symmetry-breaking gap to Kibble–Zurek mechanism
journal, January 2020


Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control
journal, October 2017


Nonequilibrium self-energy functional approach to the dynamical Mott transition
journal, June 2016


Nonequilibrium critical dynamics in the quantum chiral clock model
journal, May 2019


Direct Lattice Shaking of Bose Condensates: Finite Momentum Superfluids
journal, May 2017


Nonequilibrium self-energy functional approach to the dynamical Mott transition
text, January 2016