Entanglement spectrum of random-singlet quantum critical points

Fagotti, Maurizio; Calabrese, Pasquale; Moore, Joel E.

doi:10.1103/physrevb.83.045110

Cited by 87 publications

(138 citation statements)

References 92 publications

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“…3 we report the numerical data at L lat = 101 in zero magnetic field against our new prediction Eq. (40). Being L lat odd, the ground state is not exactly at half-filling but at ν = (L lat − 1)/2L lat .…”

Section: Corrections To the Asymptotic Behavior And Universal Fss In mentioning

confidence: 97%

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

Calabrese¹,

Mintchev²,

Vicari³

2011

J. Stat. Mech.

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128

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Abstract.We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a finite number of particles N , the Rényi entanglement entropies grow as ln N , with a prefactor that is given by the central charge. We apply this novel technique to the ground state and to excited states of periodic systems. We also consider systems with boundaries. We derive universal formulas for the leading behavior and for subleading corrections to the scaling. The universality of the results allows us to make predictions for the finite-size scaling forms of the corrections to the scaling.arXiv:1107.3985v2 [cond-mat.stat-mech]

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Section: Corrections To the Asymptotic Behavior And Universal Fss In mentioning

confidence: 97%

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

Calabrese¹,

Mintchev²,

Vicari³

2011

J. Stat. Mech.

Self Cite

128

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“…Entanglement spectra in other systems have also been explored; see, for instance, Refs. [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Bulk-edge correspondence in entanglement spectra

et al. 2011

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Li and Haldane conjectured and numerically substantiated that the entanglement spectrum of the reduced density matrix of ground-states of time-reversal breaking topological phases (fractional quantum Hall states) contains information about the counting of their edge modes when the groundstate is cut in two spatially distinct regions and one of the regions is traced out. We analytically substantiate this conjecture for a series of FQH states defined as unique zero modes of pseudopotential Hamiltonians by finding a one to one map between the thermodynamic limit counting of two different entanglement spectra: the particle entanglement spectrum (PES), whose counting of eigenvalues for each good quantum number is identical to the counting of bulk quasiholes (up to accidental zero eigenvalues of the reduced density matrix), and the orbital entanglement spectrum (OES), considered by Li and Haldane. By using a set of clustering operators which have their origin in conformal field theory (CFT) operator expansions, we show that the counting of the OES eigenvalues in the thermodynamic limit must be identical to the counting of quasiholes in the bulk . The latter equals the counting of edge modes at a hard-wall boundary placed on the sample. Our results can be interpreted as a bulk-edge correspondence in entanglement spectra. Moreover, we show that the counting of the PES and OES is identical even for CFT states which are likely bulk gapless, such as the Gaffnian wavefunction.

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“…The scaling of entanglement entropy with subsystem size has yielded a wealth of interesting results for both gapped and critical systems [3,[6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Alternatively, detailed information about the structure of entanglement can be obtained by studying the full spectrum of eigenvalues of the reduced density matrix, specifically through the eigenvalues of the "entanglement Hamiltonian"Ĥ A defined byρ A = e −ĤA /Tr(e −ĤA ) [20][21][22][23][24][25][26][27][28][29][30][31][32]. A slightly different formulation of the concept of entanglement Hamiltonians was also considered earlier in Refs.…”

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confidence: 99%

Bipartite fluctuations as a probe of many-body entanglement

et al. 2012

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We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

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Entanglement spectrum of random-singlet quantum critical points

Cited by 87 publications

References 92 publications

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

Bulk-edge correspondence in entanglement spectra

Bipartite fluctuations as a probe of many-body entanglement

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