Criticality and entanglement in random quantum systems

Refael, Gil; Moore, Joel E.

doi:10.1088/1751-8113/42/50/504010

Cited by 103 publications

(109 citation statements)

References 93 publications

(253 reference statements)

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“…The latter model belongs to the universality class known as the random singlet phase. The Renyi entropies of this phase differ from that of the uniform AFH model given by the SU(2) 1 model [15,16].…”

Section: Relation To the Haldane-shastry Modelmentioning

confidence: 71%

Quantum spin Hamiltonians for theSU(2)_kWZW model

Nielsen¹,

Cirac²,

Sierra³

2011

J. Stat. Mech.

154

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Abstract. We propose to use null vectors in conformal field theories to derive model Hamiltonians of quantum spin chains and corresponding ground state wave function(s). The approach is quite general, and we illustrate it by constructing a family of Hamiltonians whose ground states are the chiral correlators of the SU (2) k WZW model for integer values of the level k. The simplest example corresponds to k = 1 and is essentially a nonuniform generalization of the Haldane-Shastry model with long-range exchange couplings. At level k = 2, we analyze the model for N spin 1 fields. We find that the Renyi entropy and the two-point spin correlator show, respectively, logarithmic growth and algebraic decay. Furthermore, we use the null vectors to derive a set of algebraic, linear equations relating spin correlators within each model. At level k = 1, these equations allow us to compute the two-point spin correlators analytically for the finite chain uniform Haldane-Shastry model and to obtain numerical results for the nonuniform case and for higher-point spin correlators in a very simple way and without resorting to Monte Carlo techniques.

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Section: Relation To the Haldane-shastry Modelmentioning

confidence: 71%

Quantum spin Hamiltonians for theSU(2)_kWZW model

Nielsen¹,

Cirac²,

Sierra³

2011

J. Stat. Mech.

154

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“…One possibility is to study the entanglement properties of the model 43 which can be well performed within the frame of the SDRG approach. 44 At present conflicting theoretical predictions are available about the finite-size dependence of the critical entanglement entropy, 16,17 which could be possibly clarified by using larger systems in the calculation. A second promising direction of application of our approach is to consider higher dimensional systems.…”

Section: Discussionmentioning

confidence: 99%

Renormalization group study of the two-dimensional random transverse-field Ising model

2010

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The infinite-disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to L = 2048. We have calculated sample dependent pseudocritical points and studied their distribution, which is found to be characterized by the same shift and width exponent: = 1.24͑2͒. For different types of disorder the infinite-disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: x = 0.982͑15͒ and = 0.48͑2͒. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases.

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“…At the same time the study of the interplay between disorder and entanglement became a fruitful research area 4,48 . For instance, in Ref.…”

Section: Introductionmentioning

confidence: 99%

Entanglement negativity in random spin chains

2016

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We investigate the logarithmic negativity in strongly-disordered spin chains in the random-singlet phase. We focus on the spin-1/2 random Heisenberg chain and the random XX chain. We find that for two arbitrary intervals the disorder-averaged negativity and the mutual information are proportional to the number of singlets shared between the two intervals. Using the strong-disorder renormalization group (SDRG), we prove that the negativity of two adjacent intervals grows logarithmically with the intervals length. In particular, the scaling behavior is the same as in conformal field theory, but with a different prefactor. For two disjoint intervals the negativity is given by a universal simple function of the cross ratio, reflecting scale invariance. As a function of the distance of the two intervals, the negativity decays algebraically in contrast with the exponential behavior in clean models. We confirm our predictions using a numerical implementation of the SDRG method. Finally, we also implement DMRG simulations for the negativity in open spin chains. The chains accessible in the presence of strong disorder are not sufficiently long to provide a reliable confirmation of the SDRG results.

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Criticality and entanglement in random quantum systems

Cited by 103 publications

References 93 publications

Quantum spin Hamiltonians for theSU(2)_kWZW model

Quantum spin Hamiltonians for theSU(2)_kWZW model

Renormalization group study of the two-dimensional random transverse-field Ising model

Entanglement negativity in random spin chains

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Criticality and entanglement in random quantum systems

Cited by 103 publications

References 93 publications

Quantum spin Hamiltonians for theSU(2)kWZW model

Quantum spin Hamiltonians for theSU(2)kWZW model

Renormalization group study of the two-dimensional random transverse-field Ising model

Entanglement negativity in random spin chains

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Quantum spin Hamiltonians for theSU(2)_kWZW model

Quantum spin Hamiltonians for theSU(2)_kWZW model