Triangular lattice quantum dimer model with variable dimer density

Yan, Zheng; Samajdar, Rhine; Wang, Yan-Cheng; Sachdev, Subir; Meng, Zi Yang

doi:10.1038/s41467-022-33431-5

Cited by 29 publications

(7 citation statements)

References 51 publications

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“…As known in closed system, the spectral function S ( ω ) for physical observable, represented as , can be written by the eigenstates with the eigenvalue E n of the Hamiltonian , Therefore, there is a relation between energy spectrum S ( ω ) and imaginary time correlation G ( τ ) as . The K ( ω , τ ) is a kernel with slightly different expressions for bosonic/fermionic 66 – 76 . The energy spectrum of the corresponding operator can be analytically continued from the correlation function in imaginary time.…”

Section: Resultsmentioning

confidence: 99%

“…This paper is a response to these open questions and recent developments. Here we develop a protocol to overcome the exponential growth of computational complexity in obtaining the ES via QMC combined with stochastic analytic continuation 66 – 76 . Then, we test the method on a Heisenberg ladder with long entangling region between two coupled chains.…”

Section: Introductionmentioning

confidence: 99%

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Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Yan

Meng

2023

Nat Commun

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Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations. We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane’s conjecture on entanglement spectrum of topological phase. We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases. Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the (2 + 1)D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of β, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Yan

Meng

2023

Nat Commun

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“…The out-of-equilibrium dynamics of such systems leading to realization of the central role of quantum scars in such dynamics have also been studied both theoretically [38][39][40][41][42][43] and experimentally [26]. These studies have also been extended to twodimensional (2D) arrays of Rydberg atoms leading to the possibility of realization of Kitaev spin liquids in these systems [44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

“…In all of the above-mentioned studies [25][26][27][28][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], detuning of the Rydberg atoms have been assumed to be uniform. However, recently, chains of such Rydberg atoms in the presence of an additional staggered detuning have also been studied extensively [50][51][52][53][54][55][56][57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning

et al. 2023

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^{87} Rb87Rb atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction V_{{r} {r'}}Vrr′ between excited atoms at sites {r}r and {r'}r′. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes \DeltaΔ and \lambdaλ respectively. We show that when V_{{r r'}} \gg(\ll) \Delta, \lambdaVrr′≫(≪)Δ,λ for |{r}-{r'}|=1(>1)|r−r′|=1(>1), these ladders host a plateau for a wide range of \lambda/\Deltaλ/Δ where the ground states are selected by a quantum order-by-disorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density 1/41/4. Our study further unravels the presence of an emergent Ising transition stabilized via the order-by-disorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning \lambda_c/\Delta=1/3λc/Δ=1/3 which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential V_{{r} {r'}} = V_0 /|{r}-{r'}|^6Vrr′=V0/|r−r′|6, demonstrate that it survives for a wide range of V_0V0, and provide analytic estimate of \lambda_cλc as a function of V_0V0. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.

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“…Moreover, recently the field of LR quantum-many systems becomes even more active due to their fast experimental realizations, such as the Rydberg atom arrays with long-range van der Waals or dipole-dipole interaction where topological ordered state of matter and quantum criticality have been realized [17][18][19][20], magic angle twisted bilayer Graphene (TBG) and other 2D quantum moiré materials in which flat-band topology and longrange Coulomb interaction give rise to a plethora of correlated phases beyond semi-classical or band-theory description , as well as the quantum gases coupled to optical cavities [72] and many other programmable quantum simulators [73][74][75][76][77][78].…”

mentioning

confidence: 99%

Dynamical properties of quantum many-body systems with long range interactions

Song¹,

Jing-bo²,

Zhou³

et al. 2023

Preprint

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Employing large-scale quantum Monte Carlo simulations, we systematically compute the energy spectra of the 2D spin-1/2 Heisenberg model with long-range interactions. With the 1/r α ferromagnetic and staggered antiferromagnetic interactions, we find the explicit range in α for the Goldstone-type (gapless) and Higgs-type (gapped) spectra. Accompanied by the spin wave analysis, our results vividly reveal how the long-range interactions induce a mass to the Goldstone mode via the generalized Higgs mechanism. This work provides the first set of unbiased dynamical properties of long-range quantum many-body systems and suggests that many universally accepted low-energy customs for short-range systems need to be substantially modified for long-range ones which are of immediate relevance to the ongoing experimental efforts from quantum simulators to 2D quantum moiré materials.

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Triangular lattice quantum dimer model with variable dimer density

Cited by 29 publications

References 51 publications

Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning

Dynamical properties of quantum many-body systems with long range interactions

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