Floquet quantum criticality

Berdanier, William; Kolodrubetz, Michael; Parameswaran, S. A.; Vasseur, Romain

doi:10.1073/pnas.1805796115

Cited by 44 publications

(41 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…45 are analyzed in [198] and can be considered as a direct generalization of the Fisher RG rules. More generally, the phase-transitions between different Floquet-Localized-phases are expected to be controlled by Infinite-Disorder-Fixed-Points that can be sudied via SDRG [199,200].…”

Section: Floquet Dynamics Of Periodically Driven Chains In Theirmentioning

confidence: 99%

Strong disorder RG approach – a short review of recent developments

Iglói

Monthus

2018

Eur. Phys. J. B

View full text Add to dashboard Cite

Relations between SDRG and Entanglement-Algorithms 10 VI. Localized and Many-Body-Localized Phases of quantum spin chains 11 A. RSRG-X for excited eigenstates 11 B. RSRG-t for the unitary dynamics 11 C. Non-equilibrium dynamical scaling of observables 12 D. Comparison with other RG procedures existing in the field of Many-Body-Localization 13 VII. Floquet dynamics of periodically driven chains in their localized phases 13 VIII. Open dissipative quantum spin chains 13 A. Quantum spin chains coupled to a bath of quantum oscillators 13 B. Lindblad dynamics for random quantum spin chains 14 IX. Anderson localization models 14 X. Random contact process 14 A. Strong disorder RG rules 15 B. Long range spreading 15 C. Temporal disorder 15 XI. Classical master equations 16 A. Real-space renormalization for random walks in random media 16 B. RG in configuration-space for the dynamics of classical many-body models 16 XII. Random classical oscillators 17 A. Random elastic networks 17 B. Synchronisation of interacting non-linear dissipative classical oscillators 17 XIII. Other classical models 17 A. Equilibrium properties of random systems 17 B. Extremes of stochastic processes 18 XIV. Conclusion 18

show abstract

Section: Floquet Dynamics Of Periodically Driven Chains In Theirmentioning

confidence: 99%

Strong disorder RG approach – a short review of recent developments

Iglói

Monthus

2018

Eur. Phys. J. B

View full text Add to dashboard Cite

show abstract

“…However, frameworks for full characterisation of generic many-body quantum systems via all the eigenstates of the Hamiltonian governing the system continue to elude us. This issue has recently gained prominence, as it has been realised that the notion of quantum criticality is not just limited to ground states, but extends to arbitrary excited eigenstates with finite energy densities [5][6][7][8] and even to out-of-equilibrium systems [9][10][11][12][13][14]. At the heart of much of this lies the physics of many-body localisation, where eigenstates at arbitrary energy densities of disordered interacting quantum systems undergo a localisation transition at a critical value of the disorder strength which may depend on the energy density [5,[15][16][17][18][19][20][21][22][23] (see Refs.…”

Section: Introductionmentioning

confidence: 99%

Percolation in Fock space as a proxy for many-body localization

2019

View full text Add to dashboard Cite

We study classical percolation models in Fock space as proxies for the quantum many-body localisation (MBL) transition. Percolation rules are defined for two models of disordered quantum spin-chains using their microscopic quantum Hamiltonians and the topologies of the associated Fock-space graphs. The percolation transition is revealed by the statistics of Fock-space cluster sizes, obtained by exact enumeration for finite-sized systems. As a function of disorder strength, the typical cluster size shows a transition from a volume law in Fock space to sub-volume law, directly analogous to the behaviour of eigenstate participation entropies across the MBL transition. Finitesize scaling analyses for several diagnostics of cluster size statistics yield mutually consistent critical properties. We show further that local observables averaged over Fock-space clusters also carry signatures of the transition, with their behaviour across it in direct analogy to that of corresponding eigenstate expectation values across the MBL transition. The Fock-space clusters can be explored under a mapping to kinetically constrained models. Dynamics within this framework likewise show the ergodicity-breaking transition via Monte Carlo averaged local observables, and yield critical properties consistent with those obtained from both exact cluster enumeration and analytic results derived in our recent work [arXiv:1812.05115]. This mapping allows access to system sizes two orders of magnitude larger than those accessible in exact enumerations. Simple physical pictures based on freezing of local real-space segments of spins are also presented, and shown to give values for the critical disorder strength and correlation length exponent ν consistent with numerical studies.

show abstract

“…which simply counts the skyrmion number in k− space associated with thed-vector in Eq. (12). The corresponding Wannier state correlation function takes the form [30][31][32]…”

mentioning

confidence: 99%

Unifying topological phase transitions in non-interacting, interacting, and periodically driven systems

Molignini

Читра

Chen

2020

EPL

View full text Add to dashboard Cite

Topological phase transitions occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and driving, and hence require a variety of techniques and concepts to describe their topological properties. For instance, topology may be accessed from single-particle Bloch wave functions, Green's functions, or many-body wave functions. We demonstrate that despite this diversity, all topological phase transitions display a universal feature: namely, a divergence of the curvature function that composes the topological invariant at the critical point. This feature can be exploited via a renormalization-group-like methodology to describe topological phase transitions. This approach serves to extend notions of correlation function, critical exponents, scaling laws and universality classes used in Landau theory to characterize topological phase transitions in a unified manner.

show abstract

Floquet quantum criticality

Cited by 44 publications

References 69 publications

Strong disorder RG approach – a short review of recent developments

Strong disorder RG approach – a short review of recent developments

Percolation in Fock space as a proxy for many-body localization

Unifying topological phase transitions in non-interacting, interacting, and periodically driven systems

Contact Info

Product

Resources

About