Effects of quantum entanglement in phase transitions

Physical Review A, 2004

The phase diagram of spins 1/2 embedded in a magnetic field mutually interacting antiferromagnetically is determined. Contrary to the ferromagnetic case where a second order quantum phase transition occurs, a first order transition is obtained at zero field. The spectrum is computed for a large number of spins and allows one to study the ground state entanglement properties which displays a jump of its concurrence at the critical point.

To demonstrate the role played by the von Neumann entropy spectra in phase transitions we investigate the one-dimensional spin-orbital SU(2)⊗XXZ model with negative exchange parameter and anisotropic XXZ orbital interactions. When the orbital interactions are Ising-like a novel phase with spin-singlet dimer correlations and large spin-orbital entanglement entropy is found, while all the other phases are disentangled. For anisotropic XXZ orbital interactions the antiferro-spin/alternating-orbital phase becomes also entangled and inherits dimer correlations by proximity to the dimer phase. This phase provides a unique example of coupled order parameters which change the character of the phase transition from first-order to continuous. Thus we demonstrate that the von Neumann entropy spectral function is a valuable tool to identify the change of character of elementary excitations and of ground state degeneracies at quantum phase transitions.

Journal of Physics: Condensed Matter, 2006

We present a study of magnetic field induced quantum phase transitions in insulating systems. A generalized scaling theory is used to obtain the temperature dependence of several physical quantities along the quantum critical trajectory (H = H C , T → 0) where H is a longitudinal external magnetic field and H C the critical value at which the transition occurs. We consider transitions from a spin liquid at a critical field H C1 and from a fully polarized paramagnet, at H C2 , into phases with long range order in the transverse components. The transitions at H C1 and H C2 can be viewed as Bose-Einstein condensations of magnons which however belong to different universality classes since they have different values of the dynamic critical exponent. Finally, we use that the magnetic susceptibility is an entanglement witness to discuss how this type of correlation sets in as the system approaches the quantum critical point along the critical trajectory, H = H C2 , T → 0.

150 Years Of Quantum Many-Body Theory - A Festschrift in Honour of the 65th Birthdays of John W Clark, Alpo J Kallio, Manfred L Ristig and Sergio Rosati, 2001

We discuss the influence of strong quantum fluctuations on zero-temperature phase transitions in a two-dimensional spin-half Heisenberg system. Using a high-order coupled cluster treatment, we study competition of magnetic bonds with and without frustration. We find that the coupled cluster treatment is able to describe the zero-temperature transitions in a qualitatively correct way, even if frustration is present and other methods such as quantum Monte Carlo fail.

The European Physical Journal D, 2006

We consider a quantum many-body system made of N interacting S=1/2 spins on a lattice, and develop a formalism which allows to extract, out of conventional magnetic observables, the quantum probabilities for any selected spin pair to be in maximally entangled or factorized two-spin states. This result is used in order to capture the meaning of entanglement properties in terms of magnetic behavior. In particular, we consider the concurrence between two spins and show how its expression extracts information on the presence of bipartite entanglement out of the probability distributions relative to specific sets of two-spin quantum states. We apply the above findings to the antiferromagnetic Heisenberg model in a uniform magnetic field, both on a chain and on a two-leg ladder. Using Quantum Monte Carlo simulations, we obtain the above probability distributions and the associated entanglement, discussing their evolution under application of the field.

Physical Review Letters, 2008

We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and unbalanced bipartitions. It also unveils an unexpected feature of the system, namely the existence of two phase transitions, characterized by different spectra of the density matrices. One of the critical phases is described by the statistical mechanics of random surfaces, the other is a second-order phase transition.

Physical Review Letters, 2006

We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al.

Physica Scripta, 2020

We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 1-D Heisenberg frustrated J 1-J 2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α = J 2/J 1 ≈ 0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 8 sites to 16 sites, and the value of α at which the change in entanglement is observed, asymptotically tends to a value α c ≈ 0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 1-D Heisenberg frustrated J 1-J 2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 2...

Physical Review A, 2012

We study the magnetic field dependence of the entanglement entropy in quantum phase transition induced by a quench of the XX, XXX and the LMG model. The entropy for a block of L spins with the rest follows a logarithmic scaling law where the block size L is restricted due to the dependence of the prefactor on the quench time. Within this restricted region the entropy undergoes a renormalization group (RG) flow. From the RG flow equation we have analytically determined the magnetic field dependence of the entropy.

2009

We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.