Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations

Hastings, Matthew B.; González, I.; Kallin, Ann B.; Melko, Roger G.

doi:10.1103/physrevlett.104.157201

Cited by 362 publications

(473 citation statements)

References 14 publications

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“…Indeed, by measuring the expectation value of a "swap operator," 48 VMC can be used to calculate 49 the Rényi entropies S α for integer α ≥ 2. As such, we now focus on the scaling of S 2 in both the VMC and DMRG for points within the d-metal phase.…”

Section: Entanglement Entropy Resultsmentioning

confidence: 99%

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Jiang

Block

Mishmash

et al. 2012

Nature

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Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's celebrated Fermi liquid theory is of central importance to many outstanding problems in condensed matter physics. Perhaps the most important such pursuit is a full microscopic characterization of the high-Tc cuprate superconductors, where the so-called "strange metal" behavior above Tc near optimal doping is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of such a strange metal quantum phase could possibly shed new light on the interesting low-temperature behavior in the pseudogap regime and on the d-wave superconductor itself. Here, we present a theory for a specific example of a strange metal, which we term the "d-wave metal." Using variational wave functions, gauge theoretic arguments, and ultimately large-scale DMRG calculations, we establish compelling evidence that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian: the venerable t-J model supplemented with a frustrated electron ring-exchange term, which we study extensively here on the two-leg ladder. These findings constitute one of the first explicit examples of a genuine non-Fermi liquid metal existing as the ground state of a realistic model.Over the past several decades, experiments on strongly correlated materials have routinely revealed, in certain parts of the phase diagram, conducting liquids with physical properties qualitatively inconsistent with Landau's Fermi liquid theory. 1 Examples of these so-called non-Fermi liquid metals 2 include the strange metal phase of the cuprate superconductors 3,4 and heavy fermion materials near a quantum critical point. 5,6 However, such non-Fermi liquid behavior has been notoriously challenging to characterize theoretically, largely owing to the failure of a weakly interacting quasiparticle description. It is even ambiguous to define a non-Fermi liquid, although possible deviations from Fermi liquid theory include, for example, violation of Luttinger's 7 famed volume theorem, vanishing quasiparticle weight, and/or anomalous thermodynamics and transport. 5,[8][9][10][11][12] This theoretical quandary is rather unfortunate as it is likely prohibiting a full understanding of the mechanism behind high-temperature superconductivity, as well as stymying theoretically-guided searches for new exotic materials.Pioneering early theoretical work on the cuprates relied on two main premises, 3,13-17 from which we will be guided but not constrained in our pursuit and understanding of a particular non-Fermi liquid metal: (1) that the microscopics can be described by the square lattice Hubbard model with on-site Coulomb repulsion, which at strong coupling reduces in its simplest form to the t-J model; and (2) that the physics of the system can be faithfully represented by the "slave-boson" technique, wherein the physical electron operator is written as a product of a slave boson ("chargon"), which carries the electronic char...

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Section: Entanglement Entropy Resultsmentioning

confidence: 99%

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Jiang

Block

Mishmash

et al. 2012

Nature

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“…Here, we assume that L > l. We investigate the evolution of second Rényi entropy with t 1 for this state. 7 We can compute it as we explained above. We just have to change t 2 to t 1 in (3.21).…”

Section: Simultaneous Casementioning

confidence: 99%

“…It is a useful tool when we investigate the distinctive features of various quantum states. For example, it gives us the method of classifying the quantum structure of several states in condensed matter physics, e.g., [1][2][3][4][5][6][7]. The quantum entanglement is expected to be an important quantity which may shed light on the mechanism behind the AdS/CFT correspondence, e.g., [8][9][10][11].…”

Section: Contentsmentioning

confidence: 99%

Notes on quantum entanglement of local operators

Nozaki

2014

J. High Energ. Phys.

140

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This is an expanded version of the short report arXiv:1401.0539, where we studied the time evolution of (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. In the present paper, we introduce (Renyi) entanglement entropies of given local operators which are defined by late time values of excesses of (Renyi) entanglement entropies. They measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. We explain how to compute them in free massless scalar field theories and we also investigate their time evolution. Our results can be interpreted in terms of the relativistic propagation of entangled pairs. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. That operator is constructed of only the scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. These specific operators are constructed of single-species operators. We also argue that general operators obey the sum rule which we mentioned above.

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“…On the other hand, the breaking of a continuous symmetry gives rise to additive logarithmic corrections to the entropy, 14 which, for instance, have been observed numerically in the 2D Heisenberg antiferromagnet on the square lattice. [69][70][71] At the level of the ES, these corrections are associated with the TOS structure, while the area law arises from ES levels above the entanglement gap. Note that the entanglement gap is typically large deep in a SU(2)-broken phase (see Sec.…”

Section: A Tos-es Correspondencementioning

confidence: 99%

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

et al. 2013

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In magnetically ordered systems, the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite-size energy spectra, the so-called tower of states (TOS). In the present work, we numerically demonstrate that there is a correspondence between the SU(2) tower of states and the lower part of the ground-state entanglement spectrum (ES). Using state-of-the-art density matrix renormalization group (DMRG) calculations, we examine the ES of the 2D antiferromagnetic J 1 -J 2 Heisenberg model on both the triangular and kagome lattice. At large ferromagnetic J 2 , the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behavior (level counting, finite-size scaling in the thermodynamic limit) sharply reflects TOS features, and is characterized in terms of an effective entanglement Hamiltonian that we provide. At large system sizes, TOS levels are divided from the rest by an entanglement gap. Our analysis suggests that (TOS) entanglement spectroscopy provides an alternative tool for detecting and characterizing SU(2)-broken phases using DMRG.

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Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations

Cited by 362 publications

References 14 publications

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Notes on quantum entanglement of local operators

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

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