Optics and Spectroscopy

Entanglement of fermions at quantum criticality

Henrik Johannesson, D. Larsson

Published Jul 1, 2007• 0 citations

Abstract

The study of entanglement properties of quantum critical many-particle systems has become a subject of intense interest. While the basic features of entanglement scaling for critical spin-1/2 systems (coupled qubits) are by now fairly well understood, entanglement properties of critical fermions (or bosons) are less well studied. In an effort to contribute to this problem, we have analyzed the single-site entanglement of a generic spin-1/2 lattice fermion system and found that (under certain provisos) this measure can be used as a reliable marker to identify and partly characterize a quantum critical point. We illustrate our findings by exact analytical results for the single-site entanglement at the magnetic and Mott-Hubbard transitions of the 1D Hubbard model and at the Mott-Hubbard transitions of the 1D Hubbard model with long-range hopping.

DOI: 10.1134/s0030400x07070041

Related papers

Single-site entanglement of fermions at a quantum phase transition

Daniel Larsson, Henrik Johannesson

We show that the single-site entanglement of a generic spin-1/2 fermionic lattice system can be used as a reliable marker of a finite-order quantum phase transition, given certain provisos. We discuss the information contained in the single-site entanglement measure, and provide illustrations from the Mott--Hubbard metal-insulator transitions of the one-dimensional (1D) Hubbard model, and the (1D) Hubbard model with long-range hopping.

arXiv:quant-ph/0602048Physical Review AApr 25, 200672 citations

Single-site entanglement as a marker for quantum phase transitions at nonzero temperatures

Willdauany C. de Freitas da Silva, Andressa R. Medeiros-Silva, Rubem Mondaini +2 more

Entanglement has been widely investigated in condensed-matter systems since they are considered good candidates for developing quantum technologies. Additionally, entanglement is a powerful tool to explore quantum phase transitions in strongly correlated systems, with the von Neumann entropy being considered a proper measure of quantum entanglement for pure bipartite systems. For lattice systems, in particular, the single-site entanglement quantifies how much information about the quantum state of the remaining sites can be obtained by a measurement at a single site. Here, we use quantum Monte Carlo calculations to obtain the average single-site entanglement for the two-dimensional Hubbard model in different geometries, probing the effects of varying temperature and interaction strength. We find that the average single-site entanglement signals the quantum phase transitions in such systems, allowing us to identify and characterize signatures of quantum phase transitions even at finite temperatures. We also analyze the relation between entanglement and magnetic susceptibility: in all the geometries considered, we find regimes in which the quantities are roughly linearly connected, revealing their link to the Mott transition.

Physical Review ANov 21, 20250 citations

Entanglement Hamiltonians for non-critical quantum chains

Viktor Eisler, Giuseppe Di Giulio, Erik Tonni C +1 more

Abstract We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the entanglement Hamiltonian describes again free bosons or fermions and is obtained from the correlation functions via high-precision numerics for up to several hundred sites. Far away from criticality, the dominant on-site and nearest-neighbour terms have triangular profiles that can be understood from the analytical results for a half-infinite interval. Near criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.

arXiv:2007.01804Journal of Statistical Mechanics Theory and ExperimentOct 1, 202043 citations

Entanglement Hamiltonians for non-criticalquantum chains

Viktor Eisler, Giuseppe Di Giulio, Erik Tonni C +1 more

We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the entanglement Hamiltonian describes again free bosons or fermions and is obtained from the correlation functions via high-precision numerics for up to several hundred sites. Far away from criticality, the dominant on-site and nearest-neighbour terms have triangular profiles that can be understood from the analytical results for a half-infinite interval. Near criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.

Jan 1, 202029 citations

Entanglement in fermionic systems at a quantum phase transition

Henrik Johannesson, D. Larsson

We consider recent results on the use of the single-site entanglement measure for identifying and characterizing a quantum phase transition in systems of interacting fermions. We discuss the extension of these results to fermionic models where the single-site entanglement may fail to signal a quantum phase transition, with particular attention given to the one-dimensional extended UV Hubbard model.

Low Temperature PhysicsNov 1, 20078 citations

Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory.

Andrey A. Bagrov, Mikhail Danilov, Sergey Brener +3 more

A considerable success in phenomenological description of [Formula: see text] superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)-a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band t-[Formula: see text] Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds. Here, we suggest that emergence of the QCP is tightly connected with entanglement in real space and identify its location on the phase diagram of the hole-doped t-[Formula: see text] Hubbard model. To detect the QCP we study a weighted graph of inter-site quantum mutual information within a four-by-four plaquette that is solved by exact diagonalization. We demonstrate that some quantitative characteristics of such a graph, viewed as a complex network, exhibit peculiar behavior around a certain submanifold in the parametric space of the model. This method allows us to overcome difficulties caused by finite size effects and to identify precursors of the transition point even on a small lattice, where long-range asymptotics of correlation functions cannot be accessed.

Nov 24, 202015 citations