From conformal to volume law for the entanglement entropy in exponentially deformed critical spin 1/2 chains

Ramírez, Giovanni; Rodríguez-Laguna, Javier; Sierra, Germȧn

doi:10.1088/1742-5468/2014/10/p10004

Cited by 79 publications

(154 citation statements)

References 39 publications

(70 reference statements)

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“…It has been shown that a strong correlation in the noise can change the universality class and induce Griffiths singularities [15]. In some cases, inhomogeneous non-random couplings can present very large entanglement, for example, if they decay exponentially from the center, they give rise to the rainbow phase, in which singlets extend concentrically [19][20][21]. Thus, it is natural to ask about the possible fixed points of the SDRG when we consider ensembles of couplings which present long-range correlations, but are still random.New candidates to fixed points can be found by observing the statistical mechanics of the secondary structure of RNA [22].…”

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Entanglement in correlated random spin chains, RNA folding and kinetic roughening

et al. 2016

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Average block entanglement in the 1D XX-model with uncorrelated random couplings is known to grow as the logarithm of the block size, in similarity to conformal systems. In this work we study random spin chains whose couplings present long range correlations, generated as gaussian fields with a power-law spectral function. Ground states are always planar valence bond states, and their statistical ensembles are characterized in terms of their block entropy and their bond-length distribution, which follow power-laws. We conjecture the existence of a critical value for the spectral exponent, below which the system behavior is identical to the case of uncorrelated couplings. Above that critical value, the entanglement entropy violates the area law and grows as a power law of the block size, with an exponent which increases from zero to one. Interestingly, we show that XXZ models with positive anisotropy present the opposite behavior, and strong correlations in the couplings lead to lower entropies. Similar planar bond structures are also found in statistical models of RNA folding and kinetic roughening, and we trace an analogy between them and quantum valence bond states. Using an inverse renormalization procedure we determine the optimal spin-chain couplings which give rise to a given planar bond structure, and study the statistical properties of the couplings whose bond structures mimic those found in RNA folding.Under the SDRG flow, the variance of the couplings increases and its correlation length decreases, thus approaching the so-called infinite randomness fixed point (IRFP) [11]. The main question addressed in this work is: is this fixed point unique? It is known that local correlations of the couplings can be fine-tuned in order to protect entanglement [16][17][18]. Moreover, if the couplings present a diverging correlation length, we may expect new fixed points of the SDRG. It has been shown that a strong correlation in the noise can change the universality class and induce Griffiths singularities [15]. In some cases, inhomogeneous non-random couplings can present very large entanglement, for example, if they decay exponentially from the center, they give rise to the rainbow phase, in which singlets extend concentrically [19][20][21]. Thus, it is natural to ask about the possible fixed points of the SDRG when we consider ensembles of couplings which present long-range correlations, but are still random.New candidates to fixed points can be found by observing the statistical mechanics of the secondary structure of RNA [22]. A simple yet relevant model is constituted by a closed 1D chain with an even number of RNA bases, which we call sites, which are randomly coupled in pairs with indices of different parity [23,24]. Each pair constitutes an RNA bond, and the only constraint is that no bonds can cross. Therefore, the ensemble of secondary structures of RNA can be described in terms of planar bond structures, just like GSs of disordered spin-chains. Wiese and coworkers [24] studied the probability distribution...

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Entanglement in correlated random spin chains, RNA folding and kinetic roughening

et al. 2016

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“…Returning to expression (19) we can state that |D 0l | 2 = |β l | 2 and, approximately, U kl ≈ δ lk , thus obtaining Notice that the local occupation (and, therefore, the local temperature) is related to the form of the orbitals and the energy content at the site to which the detector is attached. The long-term average occupation always depends quadratically with the coupling constant, n 0 ∼ g 2 , for low enough g. Let us remark again that in order to define a proper local temperature one should always take the limit g → 0.…”

Section: Single Qubit Detectorsmentioning

confidence: 98%

Local quantum thermometry using Unruh–DeWitt detectors

Robles¹,

Rodríguez-Laguna²

2017

J. Stat. Mech.

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We propose an operational definition for the local temperature of a quantum field employing Unruh-DeWitt detectors, as used in the study of the Unruh and Hawking effects. With this definition, an inhomogeneous quantum system in equilibrium can have different local temperatures, in analogy with the Tolman-Ehrenfest theorem from general relativity. We study the local temperature distribution on the ground state of hopping fermionic systems on a curved background. The observed temperature tends to zero as the thermometer-system coupling g vanishes. Yet, for small but finite values of g, we show that the product of the observed local temperature and the logarithm of the local speed of light is approximately constant. Our predictions should be testable on ultracold atomic systems.

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“…A. The rainbow system As our physical system, we have chosen the rainbow system [25][26][27], a 1D inhomogeneous fermionic hopping system which presents volumetric entanglement between its left and right halves. It can be described on an open chain through the following Hamiltonian,…”

Section: Numerical Experimentsmentioning

confidence: 99%