Numerical study of the chiral 
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 quantum phase transition in one spatial dimension

Samajdar, Rhine; Choi, Soonwon; Pichler, Hannes; Lukin, Mikhail D.; Sachdev, Subir

doi:10.1103/physreva.98.023614

Cited by 103 publications

(146 citation statements)

References 92 publications

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“…However, it is worth noting that the best data collapse obtained up to L = 36 returns U c1 = −1.949, in agreement with Ref. 20; this clearly signals that the critical point is drifting to considerably smaller values of U as size increases [see Fig. 9(g)], in agreement with the entanglement-based diagnostics.…”

Section: B Critical Point Location Through Data Collapsesupporting

confidence: 86%

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Diagnosing Potts criticality and two-stage melting in one-dimensional hard-core boson models

et al. 2019

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We investigate a model of hard-core bosons with infinitely repulsive nearest-and next-nearestneighbor interactions in one dimension, introduced by Fendley, Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using a combination of exact diagonalization, tensor network, and quantum Monte Carlo simulations, we show how an intermediate incommensurate phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, fidelity susceptibility, correlation functions, and spectral properties. According to theoretical expectations, the disordered-to-incommensurate-phase transition point is compatible with Berezinskii-Kosterlitz-Thouless universal behavior. The second transition is instead non-relativistic, with dynamical critical exponent z > 1. For the sake of comparison, we illustrate how some of the techniques applied here work at the Potts critical point present in the phase diagram of the model for finite next-nearest-neighbor repulsion. This latter application also allows us to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy. arXiv:1901.10850v2 [cond-mat.quant-gas]

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Section: B Critical Point Location Through Data Collapsesupporting

confidence: 86%

“…In Ref. 20 , the value ν 5/7 was extracted from data collapse of the gaps, assuming the value z 4/3 for the dynamical critical exponent. This evidence was used to conclude that the transition does not belong to the PT universality class, for which ν = 1/2 and z = 2.…”

Section: A Quantum Concurrence and Fidelity Susceptibilitymentioning

confidence: 99%

Diagnosing Potts criticality and two-stage melting in one-dimensional hard-core boson models

et al. 2019

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“…Here, we explore spin models that arise naturally for ultracold atoms loaded in an optical superlattice potential together with a gradient potential. The large energy scales provided by the gradient produce a dynamical constraint, similar to projected models arising from large-scale interactions, which have recently been discussed in arrays of Rydberg atoms [8][9][10][11] and topological wires [12]. We show how these models, which can be rewritten as coupled spin chains with unusual couplings, exhibit complex critical behaviour that can be explored both in and out of equilibrium.…”

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confidence: 75%

Spin Models, Dynamics, and Criticality with Atoms in Tilted Optical Superlattices

et al. 2019

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We show that atoms in tilted optical superlattices provide a platform for exploring coupled spin chains of forms that are not present in other systems. In particular, using a period-2 superlattice in 1D, we show that coupled Ising spin chains with XZ and ZZ spin coupling terms can be engineered. We use optimized tensor network techniques to explore the criticality and non-equilibrium dynamics in these models, finding a tricritical Ising point in regimes that are accessible in current experiments. These setups are ideal for studying low-entropy physics, as initial entropy is "frozen-out" in realizing the spin models, and provide an example of the complex critical behaviour that can arise from interaction-projected models.

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“…Correspondingly, the Z 3 -symmetry breaking is believed to be in the universality class of the 3-state chiral clock model (CCM) ( Fig. 4a, Methods, and [22]).…”

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confidence: 99%

“…The exact nature of such phase transitions has been a subject of intense theoretical research for the past three decades [10,11,[22][23][24]28]. Only very recently, numerical studies of equilibrium scaling properties [22][23][24] provided evidence for a direct transition [24] along some paths across the phase boundary, where the expected range of values of the scaling exponent is µ < 0.45 [22], and µ > 0.25 [23]. Our experimental results are consistent with a direct CCM phase transition over a range of interaction strengths with µ ∼ 0.38, in agreement with the theoretical value obtained by combining the results of the most extensive numerical finite-size scaling studies [22,24] (dashed line in Fig.…”

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confidence: 99%

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

Keesling

Omran

Levine

et al. 2019

Nature

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Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations [1]. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. While time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early universe to Bose Einstein Condensates [2-5], understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is an outstanding challenge [6]. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) [7-9] for an Ising-type QPT, explore scaling universality, and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models [10,11], providing new insights into exotic systems that have not been understood previously, and opening the door for precision studies of critical phenomena, simulations of lattice gauge theories [12,13] and applications to quantum optimization [14,15].The celebrated Kibble-Zurek mechanism [2, 3] describes nonequilibrium dynamics and the formation of topological defects in a second-order phase transition driven by thermal fluctuations, and has been experimentally verified in a wide variety of physical systems [4,5]. Recently, the concepts underlying the Kibble-Zurek description have been extended to the quantum regime [7][8][9]. Here, the typical size of the correlated regions, ξ, after a dynamical sweep across the QPT scales as a power-law Critical point gc Control parameter g Correlation length » Phase 1 Phase 2 » » jg ¡ gcj ¡º Time ¿ » jg ¡ gcj ¡zº Fast ramp Slow ramp 0 1 2 3 4 5 Detuning ¢= 1 2 3 4 Interaction range RB=a ²±²±²±²±²±²±² ²±±²±±²±±²±±² ²±±±²±±±²±±±² ℤ2 ℤ3 ℤ4 t ¢ -0.05 0 0.05 -0.1 0 0.1 Density-density correlator G(r) 0 4 8 12 16 20 Distance r (sites) -0.2 -0.1 0 0.1 a b c d Ω Ω FIG. 1: Quantum Kibble-Zurek mechanism (QKZM) and phase diagram. a, Illustration of the QKZM. As the control parameter approaches its critical value, the response time, τ , given by the inverse energy gap of the system, diverges. When the temporal distance to the critical point becomes equal to the response time, as marked by red crosses, the correlation length, b, stops growing due to nonadiabatic excitations. c, Numerically calculated ground-state phase diagram. Circles (diamonds) denote numerically obtained points along the phase boundaries calculated using (infinite-size) Density-Matrix Renormalization Group techniques (Methods). The shaded regions are a guide to the eye. Dashed lines show the experimental trajectories across the phase transitions determined by the pulse diagram shown...

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Numerical study of the chiral Z3 quantum phase transition in one spatial dimension

Cited by 103 publications

References 92 publications

Diagnosing Potts criticality and two-stage melting in one-dimensional hard-core boson models

Diagnosing Potts criticality and two-stage melting in one-dimensional hard-core boson models

Spin Models, Dynamics, and Criticality with Atoms in Tilted Optical Superlattices

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

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