Quantum Information Meets Quantum Matter

Zeng, Bei; Xie, Changsheng; Zhou, D. L.; Wen, Xiao-Gang

doi:10.1007/978-1-4939-9084-9

Cited by 309 publications

(214 citation statements)

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“…2 for the case P = 1. This picture describes a 1D gauge theory in a phase with strongly fluctuating gauge fields, and is strongly reminiscent of the loop description of 2D Z 2 LGT [8,34,35].…”

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confidence: 86%

Entanglement topological invariants for one-dimensional topological superconductors

et al. 2020

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Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground state manifold, and are thus quantized to 0 or log 2. Their quantization property is inferred from the underlying lattice gauge theory description of topological superconductors, and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and non-trivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques. Panel b): quadripartite von Neumann entropy S D as a function of µ/t, U/t, at fixed ∆ = 1 and LA = LB = 12. Black lines as from Ref. [22]. The colour plot is obtained via interpolation on a 6 x 8 grid.-that can be distilled from the ground state manifold; (ii) display scaling behavior when approaching quantum phase transitions, and thus allow for the definition of entanglement critical exponents that describe the build-up of non-local quantum correlations across such transitions; (iii) are experimentally measurable in-and out-of-equilibrium utilizing recently introduced [14,15] and demonstrated [25] techniques based on arXiv:1909.04035v1 [cond-mat.supr-con]

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confidence: 86%

Entanglement topological invariants for one-dimensional topological superconductors

et al. 2020

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“…For example, a ferro/antiferro-magnetic Ising model with the constraint of having zero magnetization. In practice, one can represent these states as MPS and use well-known results [11,19] to reconstruct local parent Hamiltonians. Figure 11: Difference between numerical correlation functions computed on the JG states and the analytic formulae eq.…”

Section: A Correlation Functions and Parent Hamiltonian For The Ghz Rmentioning

confidence: 99%

“…Perhaps, among these applications, one of the most fruitful has been in the field of quantum spin liquids [16][17][18]. These are quantum phases characterized by strong correlations and longrange entanglement among arbitrary far subregions of the system [19], and for these reasons, semi-classical pictures fail in describing the phenomena involved. Variational wave functions have been used to distill generic properties such as correlation functions and entanglement [14].…”

Section: Introductionmentioning

confidence: 99%

Parent Hamiltonian reconstruction of Jastrow-Gutzwiller wavefunctions

Turkeshi

Dalmonte

2020

SciPost Phys.

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Variational wave functions have been a successful tool to investigate the properties of quantum spin liquids. Finding their parent Hamiltonians is of primary interest for the experimental simulation of these strongly correlated phases, and for gathering additional insights on their stability. In this work, we systematically reconstruct approximate spin-chain parent Hamiltonians for Jastrow-Gutzwiller wave functions, which share several features with quantum spin liquid wave-functions in two dimensions. Firstly, we determine the different phases encoded in the parameter space through their correlation functions and entanglement content. Secondly, we apply a recently proposed entanglement-guided method to reconstruct parent Hamiltonians to these states, which constrains the search to operators describing relativistic low-energy field theories -as expected for deconfined phases of gauge theories relevant to quantum spin liquids. The quality of the results is discussed using different quantities and comparing to exactly known parent Hamiltonians at specific points in parameter space. Our findings provide guiding principles for experimental Hamiltonian engineering of this class of states.

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“…Another approach, which has emerged in the last decades [20][21][22], is to characterize the system via the bipartite entanglement (BE) properties of the ground state. Entanglement between two parts of a many-body system is a pivotal figure of merit and it is analyzed typically via the Von Neumann entropy [20][21][22][23][24][25] or the entanglement spectrum [26][27][28][29][30]. An alternative approach to BE is the study of the two-body reduced density matrix [31][32][33], also quoted as pairwise entanglement.…”

Section: Introductionmentioning

confidence: 99%

“…BE has attracted large attention because it can be efficiently computed [20] and it is a resource required for classical simulations of many-body systems with numerical methods [22,34]. It has been shown that in several short-range (SR) one-dimensional models BE diverges logarithmically with the system size at criticality, whereas it does not scale in any gapped phase [20][21][22]. Instead, for LR models such a violation of the area law is found also in gapped phases [35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Multipartite-entanglement tomography of a quantum simulator

2019

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Multipartite-entanglement tomography, namely the quantum Fisher information (QFI) calculated with respect to different collective operators, allows to fully characterize the phase diagram of the quantum Ising chain in a transverse field with variable-range interaction. In particular, it recognizes the phase stemming from long-range (LR) antiferromagnetic interaction, a capability also shared by the spin squeezing. Furthermore, the QFI locates the quantum critical points, both with vanishing and nonvanishing mass gap. In this case, we also relate the finite-size power-law exponent of the QFI to the critical exponents of the model, finding a signal for the breakdown of conformal invariance in the deep LR regime. Finally, the effect of a finite temperature on the multipartite entanglement, and ultimately on the phase stability, is considered. In light of the current realizations of the model with trapped ions and of the potential measurability of the QFI, our approach yields a promising strategy to probe LR physics in controllable quantum systems.

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Quantum Information Meets Quantum Matter

Cited by 309 publications

References 0 publications

Entanglement topological invariants for one-dimensional topological superconductors

Entanglement topological invariants for one-dimensional topological superconductors

Parent Hamiltonian reconstruction of Jastrow-Gutzwiller wavefunctions

Multipartite-entanglement tomography of a quantum simulator

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