Robustness of a Perturbed Topological Phase

Dusuel, Sébastien; Kamfor, Michael; Orús, Román; Schmidt, K. P.; Vidal, Julien

doi:10.1103/physrevlett.106.107203

Cited by 152 publications

(172 citation statements)

References 35 publications

(52 reference statements)

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“…10 and Fig. 11, which also display the series expansion results both at order 10 in the low-field limit 12 and at order 5 in the high-field limit 10 . Again, the Monte Carlo data and the series expansion result are in good agreement at low fields (approximately h z < 0.34).…”

Section: Phase Diagrammentioning

confidence: 99%

“…8) develop strong non-analytic features at the transition point indicating the onset of charge condensation. To compare our data to the series expansion results, we also compute A s and σ z b using the Hellmann-Feynman theorem for the ground-state energy at order 10 in the low-field limit 12 . As can be seen in Fig.…”

Section: Phase Diagrammentioning

confidence: 99%

“…13, to larger system sizes. The behavior of TCM in a parallel field and/or a transverse field was also studied using several perturbative (high order) treatments [10][11][12] . The Monte Carlo algorithm developed in this paper suffers from the sign-problem in the presence of the transverse field component.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Phase diagram of the toric code model in a parallel magnetic field

Deng²,

Prokof’ev³

2012

Phys. Rev. B

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Ground-state phase diagram of the toric code model in a parallel magnetic field has three distinct phases: topological, charge-condensed, and vortex-condensed states. To study it we consider an implicit local order parameter characterizing the transition between the topological and chargecondensed phases, and sample it using continuous-time Monte Carlo simulations. The corresponding second-order transition line is obtained by finite-size scaling analysis of this order parameter. Symmetry breaking between charges and vortices along the first-order transition line is also observed, and our numerical result shows that the end point of the first-order transition line is located at h

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Section: Phase Diagrammentioning

confidence: 99%

Section: Phase Diagrammentioning

confidence: 99%

See 1 more Smart Citation

Phase diagram of the toric code model in a parallel magnetic field

Deng²,

Prokof’ev³

2012

Phys. Rev. B

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“…Their original manifestation, the density-matrix renormalization group (DMRG) [7], is now understood to be based on a variational update of a matrix product state (vMPS) [8,9], and has found applications in a wide range of fields such as quantum chemistry [10] and quantum information [11] as well as condensed matter physics [12]. More recent developments have extended the methods to, e.g., critical systems [13], two-dimensional lattices [14][15][16], and topologically ordered states [17].…”

Section: Introductionmentioning

confidence: 99%

Self-assembling tensor networks and holography in disordered spin chains

Goldsborough

Römer

2014

Phys. Rev. B

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We show that the numerical strong disorder renormalization group algorithm of Hikihara et al. [Phys. Rev. B 60, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions, and the entanglement entropy using the geometrical properties of the TTN. We find that the disorder-averaged spin-spin correlation scales with the average path length through the tensor network while the entanglement entropy scales with the minimal surface connecting two regions. Furthermore, the entanglement entropy increases with both disorder and system size, resulting in an area-law violation. Our results demonstrate the usefulness of a self-assembling TTN approach to disordered systems and quantitatively validate the connection between holography and quantum many-body systems.

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“…We do this by studying the eigenvalue spectra of these objects or, more precisely, of contractions of these objects, together with its associated entropy, in a way to be explained later. We provide several examples of this both for classical and quantum systems, including classical and quantum Ising, XY, XXZ and N -state Potts models, as well as several instances of 2d Projected Entangled Pair States (PEPS) [14] describing perturbed Z 2 , Z 3 , symmetry-protected, and chiral topological orders [15][16][17][18][19][20][21][22]. To achieve this goal we use a variety of TN methods for CTMs and CTs.…”

Section: Introductionmentioning

confidence: 99%

Holographic encoding of universality in corner spectra

2017

Self Cite

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In numerical simulations of classical and quantum lattice systems, 2d corner transfer matrices (CTMs) and 3d corner tensors (CTs) are a useful tool to compute approximate contractions of infinite-size tensor networks. In this paper we show how the numerical CTMs and CTs can be used, additionally, to extract universal information from their spectra. We provide examples of this for classical and quantum systems, in 1d, 2d and 3d. Our results provide, in particular, practical evidence for a wide variety of models of the correspondence between d-dimensional quantum and (d + 1)-dimensional classical spin systems. We show also how corner properties can be used to pinpoint quantum phase transitions, topological or not, without the need for observables. Moreover, for a chiral topological PEPS we show by examples that corner tensors can be used to extract the entanglement spectrum of half a system, with the expected symmetries of the SU (2) k WessZumino-Witten model describing its gapless edge for k = 1, 2. We also review the theory behind the quantum-classical correspondence for spin systems, and provide a new numerical scheme for quantum state renormalization in 2d using CTs. Our results show that bulk information of a lattice system is encoded holographically in efficiently-computable properties of its corners.

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Robustness of a Perturbed Topological Phase

Cited by 152 publications

References 35 publications

Phase diagram of the toric code model in a parallel magnetic field

Phase diagram of the toric code model in a parallel magnetic field

Self-assembling tensor networks and holography in disordered spin chains

Holographic encoding of universality in corner spectra

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