Corner transfer matrices for 2D strongly coupled many-body Floquet systems

Kukuljan, Ivan; Prosen, Tomaž

doi:10.1088/1742-5468/2016/04/043305

Cited by 6 publications

(10 citation statements)

References 25 publications

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“…8 with the correspondence H kick → T 1 H 1 . This equivalent formulation makes the link with the literature on kicked quantum models which have a long history in the field of quantum chaos (see [3,6,8,11] and references therein).…”

Section: B Periodically-kicked Quantum Spin Chainmentioning

confidence: 94%

Periodically driven random quantum spin chains: real-space renormalization for Floquet localized phases

Monthus¹

2017

J. Stat. Mech.

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When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a Block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding Strong Disorder Renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.I.

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Section: B Periodically-kicked Quantum Spin Chainmentioning

confidence: 94%

Periodically driven random quantum spin chains: real-space renormalization for Floquet localized phases

Monthus¹

2017

J. Stat. Mech.

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“…Namely, information can spread only by one site, left or right, within one period (kick of the magnetic field). Random matrix analysis [49,50] revealed that KI is chaotic.…”

mentioning

confidence: 99%

Weak quantum chaos

Kukuljan¹,

Grozdanov²,

Prosen³

2017

Phys. Rev. B

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147

126

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Out-of-time-ordered correlation functions (OTOC's) are presently being extensively debated as quantifiers of dynamical chaos in interacting quantum many-body systems. We argue that in quantum spin and fermionic systems, where all local operators are bounded, an OTOC of local observables is bounded as well and thus its exponential growth is merely transient. As a better measure of quantum chaos in such systems, we propose, and study, the density of the OTOC of extensive sums of local observables, which can exhibit indefinite growth in the thermodynamic limit. We demonstrate this for the kicked quantum Ising model by using large-scale numerical results and an analytic solution in the integrable regime. In a generic case, we observe the growth of the OTOC density to be linear in time. We prove that this density in general, locally interacting, non-integrable quantum spin and fermionic dynamical systems exhibits growth that is at most polynomial in time-a phenomenon, which we term weak quantum chaos. In the special case of the model being integrable and the observables under consideration quadratic, the OTOC density saturates to a plateau. arXiv:1701.09147v1 [cond-mat.stat-mech]

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“…A key obstacle in the search for new non-equilibrium quantum phases of matter is the tendency of closed quantum many-body systems to indefinitely absorb energy from a time-periodic driving field. Thus, in the long time limit, such systems generically reach a featureless infinite-temperature-like state with no memory of their initial conditions [1][2][3][4][5][6][7][8]. Interestingly, this infinite temperature fate can be avoided by the addition of disorder [9][10][11][12][13].…”

mentioning

confidence: 99%

Driving induced many-body localization

2017

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Subjecting a many-body localized system to a time-periodic drive generically leads to delocalization and a transition to ergodic behavior if the drive is sufficiently strong or of sufficiently low frequency. Here we show that a specific drive can have an opposite effect, taking a static delocalized system into the many-body localized phase. We demonstrate this effect using a one-dimensional system of interacting hard-core bosons subject to an oscillating linear potential. The system is weakly disordered, and is ergodic absent the driving. The time-periodic linear potential leads to a suppression of the effective static hopping amplitude, increasing the relative strengths of disorder and interactions. Using numerical simulations, we find a transition into the many-body localized phase above a critical driving frequency and in a range of driving amplitudes. Our findings highlight the potential of driving schemes exploiting the coherent destruction of tunneling for engineering long-lived Floquet phases. DOI: 10.1103/PhysRevB.96.020201Introduction. A key obstacle in the search for new nonequilibrium quantum phases of matter is the tendency of closed quantum many-body systems to indefinitely absorb energy from a time-periodic driving field. Thus, in the long time limit, such systems generically reach a featureless infinite-temperature-like state with no memory of their initial conditions [1][2][3][4][5][6][7][8]. Interestingly, this infinite temperature fate can be avoided by the addition of disorder [9][10][11][12][13]. Sufficiently strong disorder added to a clean interacting system may lead to a many-body localized (MBL) phase [14-18] which does not allow transport of energy and particles. The MBL phase can persist in the presence of a weak, high-frequency drive [9][10][11][12][13]. Periodically driven systems in the MBL phase retain memory of their initial conditions for arbitrarily long times. Thus, they can support nonequilibrium quantum phases of matter, including some which are unique to the nonequilibrium setting [19][20][21][22][23][24][25][26][27][28][29][30].Generically, subjecting an MBL system to a periodic drive increases the localization length [9][10][11]. If the driving is done at sufficiently low frequencies or high amplitudes, it may even cause the system to exit the MBL phase. This delocalization effect is caused by transitions such as photon-assisted hopping, which are mediated by the periodic drive. These transitions conserve energy only modulohω, and can therefore lead to new many-body resonances which destabilize localization.An oscillating linear potential (henceforth an ac electric field) has a more subtle effect, as it can effectively suppress the hopping amplitude between adjacent lattice sites. This effect, called dynamical localization [34] or coherent destruction of tunneling [35], has been implemented in cold atoms [36][37][38], and can be used, for example, to induce a transition from a superfluid to a Mott insulator [39,40]. In noninteracting systems, dynamical localization can be e...

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Corner transfer matrices for 2D strongly coupled many-body Floquet systems

Cited by 6 publications

References 25 publications

Periodically driven random quantum spin chains: real-space renormalization for Floquet localized phases

Periodically driven random quantum spin chains: real-space renormalization for Floquet localized phases

Weak quantum chaos

Driving induced many-body localization

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