DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Strong-disorder renormalization group for periodically driven systems

Abstract

Quenched randomness can lead to robust nonequilibrium phases of matter in periodically driven (Floquet) systems. Analyzing transitions between such dynamical phases requires a method capable of treating the twin complexities of disorder and discrete time-translation symmetry. We introduce a real-space renormalization group approach, asymptotically exact in the strong-disorder limit, and exemplify its use on the periodically driven interacting quantum Ising model. As a result, we analyze the universal physics near the critical lines and multicritical point of this model, and demonstrate the robustness of our results to the inclusion of weak interactions.

Authors:
 [1];  [2];  [3];  [4]
  1. Univ. of California, Berkeley, CA (United States)
  2. The Univ. of Texas at Dallas, Richardson, TX (United States)
  3. Univ. of Oxford, Oxford (United Kingdom)
  4. Univ. of Massachusetts, Amherst, MA (United States)
Publication Date:
Research Org.:
Univ. of Massachusetts, Amherst, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1481395
Alternate Identifier(s):
OSTI ID: 1481457
Grant/Contract Number:  
SC0019168; AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 17; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Periodically-Driven Systems; Renormalization Group; Disordered Systems; Localization

Citation Formats

Berdanier, William, Kolodrubetz, Michael, Parameswaran, S. A., and Vasseur, Romain. Strong-disorder renormalization group for periodically driven systems. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.174203.
Berdanier, William, Kolodrubetz, Michael, Parameswaran, S. A., & Vasseur, Romain. Strong-disorder renormalization group for periodically driven systems. United States. https://doi.org/10.1103/PhysRevB.98.174203
Berdanier, William, Kolodrubetz, Michael, Parameswaran, S. A., and Vasseur, Romain. Fri . "Strong-disorder renormalization group for periodically driven systems". United States. https://doi.org/10.1103/PhysRevB.98.174203. https://www.osti.gov/servlets/purl/1481395.
@article{osti_1481395,
title = {Strong-disorder renormalization group for periodically driven systems},
author = {Berdanier, William and Kolodrubetz, Michael and Parameswaran, S. A. and Vasseur, Romain},
abstractNote = {Quenched randomness can lead to robust nonequilibrium phases of matter in periodically driven (Floquet) systems. Analyzing transitions between such dynamical phases requires a method capable of treating the twin complexities of disorder and discrete time-translation symmetry. We introduce a real-space renormalization group approach, asymptotically exact in the strong-disorder limit, and exemplify its use on the periodically driven interacting quantum Ising model. As a result, we analyze the universal physics near the critical lines and multicritical point of this model, and demonstrate the robustness of our results to the inclusion of weak interactions.},
doi = {10.1103/PhysRevB.98.174203},
journal = {Physical Review B},
number = 17,
volume = 98,
place = {United States},
year = {Fri Nov 09 00:00:00 EST 2018},
month = {Fri Nov 09 00:00:00 EST 2018}
}

Journal Article:

Citation Metrics:
Cited by: 8 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields
journal, August 2014


Theory of many-body localization in periodically driven systems
journal, September 2016


Colloquium: Atomic quantum gases in periodically driven optical lattices
journal, March 2017


Topological characterization of periodically driven quantum systems
journal, December 2010


Critical Time Crystals in Dipolar Systems
journal, July 2017


Localization-protected quantum order
journal, July 2013


Floquet Engineering of Correlated Tunneling in the Bose-Hubbard Model with Ultracold Atoms
journal, May 2016


Eigenstate thermalization hypothesis
journal, July 2018


P 31 NMR study of discrete time-crystalline signatures in an ordered crystal of ammonium dihydrogen phosphate
journal, May 2018


Floquet topological insulator in semiconductor quantum wells
journal, March 2011

  • Lindner, Netanel H.; Refael, Gil; Galitski, Victor
  • Nature Physics, Vol. 7, Issue 6
  • DOI: 10.1038/nphys1926

Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
journal, May 1965


Quantum Criticality of Hot Random Spin Chains
journal, May 2015


Universal Dynamics and Renormalization in Many-Body-Localized Systems
journal, March 2015


Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering
journal, March 2015


Observation of discrete time-crystalline order in a disordered dipolar many-body system
journal, March 2017

  • Choi, Soonwon; Choi, Joonhee; Landig, Renate
  • Nature, Vol. 543, Issue 7644
  • DOI: 10.1038/nature21426

Floquet engineering with quasienergy bands of periodically driven optical lattices
journal, November 2015


Dynamical Quantum Phase Transitions in Random Spin Chains
journal, May 2014


Floquet Time Crystals
journal, August 2016


Parafermion chain with 2 π / k Floquet edge modes
journal, July 2016


Prethermal Phases of Matter Protected by Time-Translation Symmetry
journal, March 2017


Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields
journal, March 2016


Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
journal, May 2018


Localization and topology protected quantum coherence at the edge of hot matter
journal, July 2015

  • Bahri, Yasaman; Vosk, Ronen; Altman, Ehud
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8341

Floquet topological phases with symmetry in all dimensions
journal, May 2017


Random antiferromagnetic quantum spin chains
journal, August 1994


Many-body localization: An introduction and selected topics
journal, September 2018


Periodically driven ergodic and many-body localized quantum systems
journal, February 2015


Quantum Phase Transitions
book, January 2011


Classification of topological phases in periodically driven interacting systems
journal, May 2016


Discrete Time Crystals: Rigidity, Criticality, and Realizations
journal, January 2017


Abelian Floquet symmetry-protected topological phases in one dimension
journal, September 2016


Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems
journal, July 2013


Many-body localization and symmetry-protected topological order
journal, April 2014


Many-body localization phase transition
journal, November 2010


Localization of interacting fermions at high temperature
journal, April 2007


Stroboscopic symmetry-protected topological phases
journal, September 2015


Dynamics and Transport in Random Antiferromagnetic Spin Chains
journal, April 2000


Disordered XYZ spin chain simulations using the spectrum bifurcation renormalization group
journal, July 2016


Photovoltaic Hall effect in graphene
journal, February 2009


Entanglement Entropy of Random Quantum Critical Points in One Dimension
journal, December 2004


Critical behavior of random transverse-field Ising spin chains
journal, March 1995


Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states
journal, May 2006


Many-Body Localization in Periodically Driven Systems
journal, April 2015


Dynamics and transport in random quantum systems governed by strong-randomness fixed points
journal, March 2001


Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
journal, June 2016


Absolute stability and spatiotemporal long-range order in Floquet systems
journal, August 2016


Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field
journal, June 1973


Phase Structure of Driven Quantum Systems
journal, June 2016


Exponentially Slow Heating in Periodically Driven Many-Body Systems
journal, December 2015


Random transverse field Ising spin chains
journal, July 1992


Disordered Chern insulator with a two-step Floquet drive
journal, December 2016


Relation between the Anderson and Kondo Hamiltonians
journal, September 1966


Floquet–Magnus theory and generic transient dynamics in periodically driven many-body quantum systems
journal, April 2016


Periodically driven random quantum spin chains: real-space renormalization for Floquet localized phases
journal, July 2017

  • Monthus, Cécile
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 7
  • DOI: 10.1088/1742-5468/aa75dd

SNEG – Mathematica package for symbolic calculations with second-quantization-operator expressions
journal, October 2011


Many-Body Localization and Thermalization in Quantum Statistical Mechanics
journal, March 2015


Low-temperature properties of the random Heisenberg antiferromagnetic chain
journal, August 1980


Classification of Interacting Topological Floquet Phases in One Dimension
journal, October 2016

  • Potter, Andrew C.; Morimoto, Takahiro; Vishwanath, Ashvin
  • Physical Review X, Vol. 6, Issue 4
  • DOI: 10.1103/PhysRevX.6.041001

Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality
journal, March 2014


Topological singularities and the general classification of Floquet–Bloch systems
journal, December 2015


Quantum statistical mechanics in a closed system
journal, February 1991


Chaos and quantum thermalization
journal, August 1994


Defining time crystals via representation theory
journal, September 2017


Stability and instability towards delocalization in many-body localization systems
journal, April 2017


Observation of a discrete time crystal
journal, March 2017

  • Zhang, J.; Hess, P. W.; Kyprianidis, A.
  • Nature, Vol. 543, Issue 7644
  • DOI: 10.1038/nature21413

Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains
journal, December 2002


Enhancement and sign change of magnetic correlations in a driven quantum many-body system
journal, January 2018

  • Görg, Frederik; Messer, Michael; Sandholzer, Kilian
  • Nature, Vol. 553, Issue 7689
  • DOI: 10.1038/nature25135

Floquet quantum criticality
journal, August 2018

  • Berdanier, William; Kolodrubetz, Michael; Parameswaran, S. A.
  • Proceedings of the National Academy of Sciences, Vol. 115, Issue 38
  • DOI: 10.1073/pnas.1805796115

Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases
journal, June 2016


Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases
journal, June 2016


Fate of Many-Body Localization Under Periodic Driving
journal, July 2015


Enhancement and sign change of magnetic correlations in a driven quantum many-body system
text, January 2018


Photovoltaic Hall effect in graphene
text, January 2008


The many-body localization phase transition
text, January 2010


Topological characterization of periodically-driven quantum systems
text, January 2010


Dynamical quantum phase transitions in random spin chains
text, January 2013


Localization and topology protected quantum coherence at the edge of 'hot' matter
preprint, January 2013


Many body localization and thermalization in quantum statistical mechanics
text, January 2014


Fate of many-body localization under periodic driving
text, January 2014


Quantum criticality of hot random spin chains
text, January 2014


A theory of many-body localization in periodically driven systems
text, January 2014


Exponentially slow heating in periodically driven many-body systems
text, January 2015


Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms
text, January 2016


Pre-thermal phases of matter protected by time-translation symmetry
text, January 2016


Discrete time crystals: rigidity, criticality, and realizations
text, January 2016


Observation of a Discrete Time Crystal
text, January 2016


Floquet topological phases with symmetry in all dimensions
text, January 2016


Defining Time Crystals via Representation Theory
text, January 2016


Critical Time Crystals in Dipolar Systems
text, January 2017


Floquet Quantum Criticality
text, January 2018


Eigenstate Thermalization Hypothesis
text, January 2018


Dynamics and transport in random quantum systems governed by strong-randomness fixed points
text, January 2000


Localization of interacting fermions at high temperature
text, January 2006


Chaos and Quantum Thermalization
text, January 1994


Works referencing / citing this record:

Strong disorder RG approach – a short review of recent developments
journal, November 2018