SciPost Phys. 15, 202 (2023) ·
published 23 November 2023

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We show that a dynamical transition from a nonheating to a heating phase of a periodic $SL(2,\mathbb{R})$ driven two dimensional conformal field theory (CFT) with a large central charge is perceived as a first order transition by a bulk brane embedded in the dual AdS. We construct the dual bulk metric corresponding to a driven CFT for both the heating and the nonheating phases. These metrics are different AdS$_2$ slices of the pure AdS$_3$ metric. We embed a brane in the obtained dual AdS space and provide an explicit computation of its free energy both in the probe limit and for an endofworld (EOW) brane taking into account its backreaction. Our analysis indicates a finite discontinuity in the first derivative of the brane free energy as one moves from the nonheating to the heating phase (by tuning the drive amplitude and/or frequency of the driven CFT) thus demonstrating the presence of the bulk first order transition. Interestingly, no such transition is perceived by the bulk in the absence of the brane. We also provide explicit computations of twopoint, fourpoint outoftime correlators (OTOC) using the bulk picture. Our analysis shows that the structure of these correlators in different phases match their counterparts computed in the driven CFT. We analyze the effect of multiple EOW branes in the bulk and discuss possible extensions of our work for richer geometries and branes.
Anwesha Chattopadhyay, Bhaskar Mukherjee, Krishnendu Sengupta, Arnab Sen
SciPost Phys. 14, 146 (2023) ·
published 7 June 2023

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We introduce a disorderfree model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two upspins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ringexchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasionedimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum manybody scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the onedimensional PXP chain with open boundaries, a paradigmatic model for quantum manybody scarring; while the junction of two wires represents a distinct constrained model.
Madhumita Sarkar, Mainak Pal, Arnab Sen, Krishnendu Sengupta
SciPost Phys. 14, 004 (2023) ·
published 16 January 2023

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$^{87}{\rm Rb}$ atoms are known to have longlived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction $V_{{\bf r} {\bf r'}}$ between excited atoms at sites ${\bf r}$ and ${\bf r'}$. Here we study such atoms in a twoleg ladder geometry in the presence of both staggered and uniform detuning with amplitudes $\Delta$ and $\lambda$ respectively. We show that when $V_{{\bf r r'}} \gg(\ll) \Delta, \lambda$ for ${\bf r}{\bf r'}=1(>1)$, these ladders host a plateau for a wide range of $\lambda/\Delta$ where the ground states are selected by a quantum orderbydisorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density $1/4$. Our study further unravels the presence of an emergent Ising transition stabilized via the orderbydisorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning $\lambda_c/\Delta=1/3$ which agrees well with exactdiagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential $V_{{\bf r} {\bf r'}} = V_0 /{\bf r}{\bf r'}^6$, demonstrate that it survives for a wide range of $V_0$, and provide analytic estimate of $\lambda_c$ as a function of $V_0$. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.
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in Submissions  report on Quantum orderbydisorder induced phase transition in Rydberg ladders with staggered detuning