Classification of 
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 deformed Floquet conformal field theories

Han, Bo; Wen, Xueda

doi:10.1103/physrevb.102.205125

Cited by 23 publications

(35 citation statements)

References 58 publications

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“…which has also been obtained in [38,40,43,44] from a different perspective. That is to say, in the special case with SL 2 deformation, the flow equation x j+1 = f (x j ) in x-frame corresponds to a Möbius transformation in z-frame.…”

Section: Revisiting the Sl 2 Deformation And Fixed Pointssupporting

confidence: 68%

“…only v(x) is nonzero while v(x) = 0 as we have assumed for the SL 2 case in the beginning of this section. 9 For an explicit example showing this result, let us consider a the two-step driving in (44) with H 0 the homogeneous (undeformed) Hamiltonian and H 1 with v(x) = 2 sin 2 ( πqx L ), there are q pairs of fixed point in heating phase, and the period of fixed points is determined by parameter T 0 (driving time of T 0 ): for (s − 1)/q < T 0 /L < s/q where 1 s q is an integer, one can explicitly check that the period is given by p = q/gcd(q, s).…”

Section: Phase Transitionmentioning

confidence: 85%

“…[38], where the deformation is a sine-square function v(x) = v(x) = sin 2 (πx/L). This special choice has an underlying SL 2 algebraic structure that facilitates a thorough discussion on the dynamics, including the quasi-periodic and random driving cases [38][39][40][41][42][43][44][45]. In all three cases, both the non-heating and heating phases are identified, and the heating phase is found to exhibit energy-momentum peaks with linearly growing entanglement.…”

Section: Introductionmentioning

confidence: 99%

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Floquet conformal field theories with generally deformed Hamiltonians

Fan

Vishwanath

et al. 2021

SciPost Phys.

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In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a \mathfrak{sl}_2𝔰𝔩2 sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the stroboscopic trajectories of operator evolution. The presence/absence of spatial fixed points in the operator evolution indicates that the driven CFT is in a heating/non-heating phase, in which the entanglement entropy grows/oscillates in time. Additionally, the heating regime is further subdivided into a multitude of phases, with different entanglement patterns and spatial distribution of energy-momentum density, which are characterized by the number of spatial fixed points. Phase transitions between these different heating phases can be achieved simply by changing the duration of application of the driving Hamiltonian. %In general, there are rich internal structures in the heating phase characterized by different numbers of spatial fixed points, which result in different entanglement patterns and distribution of energy-momentum density in space. %Interestingly, after each driving cycle, these spatial fixed points will shuffle to each other in the array, and come back to the original locations after pp (p\ge 1p≥1) driving cycles. We demonstrate the general features with concrete CFT examples and compare the results to lattice calculations and find remarkable agreement.

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Section: Revisiting the Sl 2 Deformation And Fixed Pointssupporting

confidence: 68%

Section: Phase Transitionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

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Floquet conformal field theories with generally deformed Hamiltonians

Fan

Vishwanath

et al. 2021

SciPost Phys.

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“…More recently, several theoretical studies concentrated on the effect of Floquet dynamics on conformal field theories [32][33][34][35][36][37][38][39][40]. Usually driving a CFT is expected to generate an additional scale in the problem which drives the system away from its conformally invariant fixed point.…”

Section: Introductionmentioning

confidence: 99%

“…The main results obtained in refs. [32][33][34][35][36][37][38][39][40] can be summarized as follows. First, it was noted in ref.…”

Section: Introductionmentioning

confidence: 99%

Conformal Floquet dynamics with a continuous drive protocol

Das

Ghosh

Sengupta

2021

J. High Energ. Phys.

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We study the properties of a conformal field theory (CFT) driven periodically with a continuous protocol characterized by a frequency ωD. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator U. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for U that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability (Pn), equal (Cn) and unequal (Gn) time two-point primary correlators, energy density(En), and the mth Renyi entropy ($$ {S}_n^m $$ S n m ) after n drive cycles. Our results show that below a crossover stroboscopic time scale nc, Pn, En and Gn exhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure of Cn, Gn and En for the continuous protocol and find emergence of spatial divergences of Cn and Gn in both the heating and non-heating phases. We express our results for $$ {S}_n^m $$ S n m and Cn in terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

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Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians

Mao,

Nozaki,

Tamaoka

et al. 2024

J. High Energ. Phys.

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We explore non-equilibrium processes in two-dimensional conformal field theories (2d CFTs) due to the growth of operators induced by inhomogeneous and homogeneous Hamiltonians by investigating the time dependence of the partition function, energy density, and entanglement entropy. The non-equilibrium processes considered in this paper are constructed out of the Lorentzian and Euclidean time evolution governed by different Hamiltonians. We explore the effect of the time ordering on entanglement dynamics so that we find that in a free boson CFT and RCFTs, this time ordering does not affect the entanglement entropy, while in the holographic CFTs, it does. Our main finding is that in the holographic CFTs, the non-unitary time evolution induced by the inhomogeneous Hamiltonian can retain the initial state information longer than in the unitary time evolution.

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Classification of SL2 deformed Floquet conformal field theories

Cited by 23 publications

References 58 publications

Floquet conformal field theories with generally deformed Hamiltonians

Floquet conformal field theories with generally deformed Hamiltonians

Conformal Floquet dynamics with a continuous drive protocol

Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians

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