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Operationally accessible entanglement of 1D spinless fermions

Emanuel Casiano-Diaz

Published Jan 1, 2021• 0 citations
OpenAlex

Abstract

The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing and detecting phase transitions. It can be quantified via the von Neumann and Rényi entropies. Particle number superselection rules restrict the amount of entanglement that can be accessed as a resource. In this work, the accessible entanglement between spatial subregions of a 1D lattice of spinless fermions is quantified. Exact diagonalization results confirm the feasibility of the accessible entanglement entropy as a probe to detect quantum phase transitions.

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The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing and detecting phase transitions. It can be quantified via the von Neumann and Rényi entropies. Particle number superselection rules restrict the amount of entanglement that can be accessed as a resource. In this work, the accessible entanglement between spatial subregions of a 1D lattice of spinless fermions is quantified. Exact diagonalization results confirm the feasibility of the accessible entanglement entropy as a probe to detect quantum phase transitions.
The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing, quantum communication and detecting phase transitions, among others. The amount of entanglement can be quantified via the von Neumann and Rényi entropies, which have their origins in information theory. In this work, the quantum entanglement between subsystems of a one dimen- sional lattice model of fermions is quantified. The von Neumann and Rényi entropies were calculated for two types of subsystems. In the first study, the subsystems were treated as two subsets of particles, and in the second, as two spatial subregions. Finally, by considering particle superselection rules, the amount of entanglement that can actually be accessed as a resource was calcu- lated. In all cases, the quantum entanglement served to detect phase transitions in the model.
For indistinguishable itinerant particles subject to a superselection rule fixing their total number, a portion of the entanglement entropy under a spatial bipartition of the ground state is due to particle fluctuations between subsystems and thus is inaccessible as a resource for quantum information processing. We quantify the remaining operationally accessible entanglement in a model of interacting spinless fermions on a one-dimensional lattice via exact diagonalization and the density matrix renormalization group. We find that the accessible entanglement exactly vanishes at the first-order phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. Throughout the phase diagram, we discuss the connection between the accessible entanglement entropy and the variance of the probability distribution describing intrasubregion particle-number fluctuations.
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.097902] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Rényi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operationally accessible entanglement that is both computationally and experimentally measurable. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to 10^{5} particles.
Quantum entanglement is studied in the context of its use as a probe of quantum phases within fermionic non-interacting quantum wires. In particular, we consider the uniform lattice, as well as the Su-Schreiffer-Heeger (SSH) model, and use the bipartite entropy of entanglement to characterize their quantum phases. In 1D, it has been shown analytically that the von Neumann entropy defined for a subsystem HA⊂HA⊗HB\mathcal{H}_A \subset \mathcal{H}_A\otimes\mathcal{H}_BHA​⊂HA​⊗HB​ takes distinct forms dependent on the whether or not the state is thermodynamically gapped. It is also known that entanglement can be used to identify topological phases of a quantum system, such as the symmetry protected phase found in the SSH model. These results are confirmed numerically, and some common techniques for the calculation of bipartite entanglement are compared according to their aptitude for simulating larger and more complicated systems.
Abstract We investigate the scaling of the Rényi entanglement entropies for a particle bipartition of interacting spinless fermions in one spatial dimension. In the Tomonaga–Luttinger liquid regime, we calculate the second Rényi entanglement entropy and show that the leading order finite-size scaling is equal to a universal logarithm of the system size plus a non-universal constant. Higher-order corrections decay as power-laws in the system size with exponents that depend only on the Luttinger parameter. We confirm the universality of our results by investigating the one dimensional t − V model of interacting spinless fermions via exact-diagonalization techniques. The resulting sensitivity of the particle partition entanglement to boundary conditions and statistics supports its utility as a probe of quantum liquids.
Abstract Entanglement entropy under a particle bipartition generates complementary information to mode entanglement because it is sensitive to interactions and particle statistics at leading order and does not depend on any externally imposed length scale. In this paper, we investigate the particle entanglement entropy in a system of N interacting spinless lattice fermions in one spatial dimension by combining bosonization techniques with exact and approximate numerical methods. We introduce a general scaling form for the fermionic particle entanglement entropy captured by a shape function that enters as an extensive interaction-induced correction to a known free fermion result. A general asymptotic expansion in the total number of particles demonstrates that its form is robust for different values of the Rényi index and highlights how quantum correlations are encoded in the n-particle density matrix of a pure many-body quantum state.