1,720,981 research outputs found
Entanglement asymmetry as a probe of symmetry breaking
Full text linkSymmetry and symmetry breaking are two pillars of modern quantum physics.
Still, quantifying how much a symmetry is broken is an issue that has received
little attention. In extended quantum systems, this problem is intrinsically
bound to the subsystem of interest. Hence, in this work, we borrow methods from
the theory of entanglement in many-body quantum systems to introduce a
subsystem measure of symmetry breaking that we dub entanglement asymmetry. As a
prototypical illustration, we study the entanglement asymmetry in a quantum
quench of a spin chain in which an initially broken global symmetry is
restored dynamically. We adapt the quasiparticle picture for entanglement
evolution to the analytic determination of the entanglement asymmetry. We find,
expectedly, that larger is the subsystem, slower is the restoration, but also
the counterintuitive result that more the symmetry is initially broken, faster
it is restored, a sort of quantum Mpemba effect, a phenomenon that we show to
occur in a large variety of systems.Comment: 7 pages, 5 figures. Text reorganized, new results for interacting
integrable and non-integrable spin chains added. Final version published in
Nature Communication
Symmetry-resolved entanglement in critical non-Hermitian systems
No full textThe study of entanglement in the symmetry sectors of a theory has recently attracted a lot of attention since it provides better understanding of some aspects of quantum many-body systems. In this paper, we extend this analysis to the case of non-Hermitian models, in which the reduced density matrix rho A may be nonpositive definite and the entanglement entropy negative or even complex. Here we examine in detail the symmetry-resolved entanglement in the ground state of the non-Hermitian Su-Schrieffer-Heeger chain at the critical point, a model that preserves particle number and whose scaling limit is a bc-ghost nonunitary conformal field theory (CFT). By combining bosonization techniques in the field theory and exact lattice numerical calculations, we analytically derive the charged moments of rho A and |rho A |. From them, we can understand the origin of the nonpositiveness of rho A and naturally define a positive-definite reduced density matrix in each charge sector, which gives a well-defined symmetry-resolved entanglement entropy. As a by-product, we also obtain the analytical distribution of the critical entanglement spectrum
Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
Full text linkThe entanglement asymmetry is a novel quantity that, using entanglement
methods, measures how much a symmetry is broken in a part of an extended
quantum system. So far it has only been used to characterise the breaking of
continuous Abelian symmetries. In this paper, we extend the concept to cyclic
groups. As an application, we consider the XY spin chain, in
which the ground state spontaneously breaks the spin parity
symmetry in the ferromagnetic phase. We thoroughly investigate the
non-equilibrium dynamics of this symmetry after a global quantum quench,
generalising known results for the standard order parameter.Comment: 37 pages, 15 figures. Minor corrections and comments added, new
figure. Final version published in JSTA
An entanglement asymmetry study of black hole radiation
Full text linkHawking\u27s discovery that black holes can evaporate through radiation emission has posed a number of questions that with time became fundamental hallmarks for a quantum theory of gravity. The most famous one is likely the information paradox, which finds an elegant explanation in the Page argument suggesting that a black hole and its radiation can be effectively represented by a random state of qubits. Leveraging the same assumption, we ponder the extent to which a black hole may display emergent symmetries, employing the entanglement asymmetry as a modern, information-based indicator of symmetry breaking. We find that for a random state devoid of any symmetry, a symmetry emerges and it is exact in the thermodynamic limit before the Page time. At the Page time, the entanglement asymmetry shows a finite jump to a large value. Our findings imply that the emitted radiation is symmetric up to the Page time and then undergoes a sharp transition. Conversely the black hole is symmetric only after the Page time.6 pages, 3 figures. Comments added. Final version published in Phys. Rev.
Entanglement asymmetry and quantum Mpemba effect in the XY spin chain
Full text linkEntanglement asymmetry is a quantity recently introduced to measure how much
a symmetry is broken in a part of an extended quantum system. It has been
employed to analyze the non-equilibrium dynamics of a broken symmetry after a
global quantum quench with a Hamiltonian that preserves it. In this work, we
carry out a comprehensive analysis of the entanglement asymmetry at equilibrium
taking the ground state of the XY spin chain, which breaks the particle
number symmetry, and provide a physical interpretation of it in terms of
superconducting Cooper pairs. We also consider quenches from this ground state
to the XX spin chain, which preserves the broken symmetry. In this case,
the entanglement asymmetry reveals that the more the symmetry is initially
broken, the faster it may be restored in a subsystem, a surprising and
counter-intuitive phenomenon that is a type of a quantum Mpemba effect. We
obtain a quasi-particle picture for the entanglement asymmetry in terms of
Cooper pairs, from which we derive the microscopic conditions to observe the
quantum Mpemba effect in this system, giving further support to the criteria
recently proposed for arbitrary integrable quantum systems. In addition, we
find that the power law governing symmetry restoration depends discontinuously
on whether the initial state is critical or not, leading to new forms of strong
and weak Mpemba effects.Comment: 30 pages, 8 figure
Multi-charged moments of two intervals in conformal field theory
Full text linkWe study the multi-charged moments for two disjoint intervals in the ground
state of two dimensional CFTs with central charge and global
symmetry: the massless Dirac field theory and the compact boson (Luttinger
liquid). For this purpose, we compute the partition function on the higher
genus Riemann surface arising from the replica method in the presence of
background magnetic fluxes between the sheets of the surface. We consider the
general situation in which the fluxes generate different twisted boundary
conditions at each branch point. The obtained multi-charged moments allow us to
derive the symmetry resolution of the R\'enyi entanglement entropies and the
mutual information for non complementary bipartitions. We check our findings
against exact numerical results for the tight-binding model, which is a lattice
realisation of the massless Dirac theory.Comment: 36 pages, 7 figures. Typos corrected, references added. Final version
published in JHE
Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
No full textAbstract We investigate how entanglement in the mixed state of a quantum field theory can be described using the cross-computable norm or realignment (CCNR) criterion, employing a recently introduced negativity. We study its symmetry resolution for two disjoint intervals in the ground state of the massless Dirac fermion field theory, extending previous results for the case of adjacent intervals. By applying the replica trick, this problem boils down to computing the charged moments of the realignment matrix. We show that, for two disjoint intervals, they correspond to the partition function of the theory on a torus with a non-contractible charged loop. This confers a great advantage compared to the negativity based on the partial transposition, for which the Riemann surfaces generated by the replica trick have higher genus. This result empowers us to carry out the replica limit, yielding analytic expressions for the symmetry-resolved CCNR negativity. Furthermore, these expressions provide also the symmetry decomposition of other related quantities such as the operator entanglement of the reduced density matrix or the reflected entropy
Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover
No full textAbstract We study the Rényi entanglement entropies along the massless renormalisation group flow that connects the tricritical and critical Ising field theories. Similarly to the massive integrable field theories, we derive a set of bootstrap equations, from which we can analytically calculate the twist field form factors in a recursive way. Additionally, we also obtain them as a non-trivial ‘roaming limit’ of the sinh-Gordon theory. Then the Rényi entanglement entropies are obtained as expansions in terms of the form factors of these branch point twist fields. We find that the form factor expansion of the entanglement entropy along the flow organises in two different kind of terms. Those that couple particles with the same chirality, and reproduce the entropy of the infrared Ising theory, and those that couple particles with different chirality, which provide the ultraviolet contributions. The massless flow under study possesses a global ℤ2 spin-flip symmetry. We further consider the composite twist fields associated to this group, which enter in the study of the symmetry resolution of the entanglement. We derive analytical expressions for their form factors both from the bootstrap equations and from the roaming limit of the sinh-Gordon theory
Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
Full text linkWe consider the quantum quench in the XX spin chain starting from a tilted
N\'eel state which explicitly breaks the symmetry of the post-quench
Hamiltonian. Very surprisingly, the symmetry is not restored at large
time because of the activation of a non-Abelian set of charges which all break
it. The breaking of the symmetry can be effectively and quantitatively
characterised by the recently introduced entanglement asymmetry. By a
combination of exact calculations and quasi-particle picture arguments, we are
able to exactly describe the behaviour of the asymmetry at any time after the
quench. Furthermore we show that the stationary behaviour is completely
captured by a non-Abelian generalised Gibbs ensemble. While our computations
have been performed for a non-interacting spin chain, we expect similar results
to hold for the integrable interacting case as well because of the presence of
non-Abelian charges also in that case.Comment: 33 pages, 5 figures. Minor corrections and comments adde
- …
