Classical nature of ordered phases: origin of spontaneous symmetry breaking

Cianciaruso, Marco; Ferro, Livia; Giampaolo, Salvatore Marco; Zonzo, G.; Illuminati, Fabrizio

doi:10.48550/arxiv.1408.1412

Cited by 3 publications

(8 citation statements)

References 24 publications

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“…The long-range pairwise quantum discord between two spins in the ground state of the one-dimensional XY chain has been recently investigated in Refs. [8,[12][13][14]. It turns out that such quantity features a long-range behavior quite analogous to that of the mutual information, with the crucial difference that it vanishes identically in all possible ground states as m µ → 0.…”

Section: Comparison With Other Indicators Of Macroscopic Coherent Sup...mentioning

confidence: 90%

“…As shown in Ref. [8], all correlation functions can be associated to spin operators that either commute or anti-commute with the parity operator P µ . Therefore, the reduced density matrix ρ C (u, v) can be expressed as the sum of a symmetric part that coincides with the density matrix of the symmetric ground state, ρ…”

Section: On Products Of Pauli Matrices σ I Amentioning

confidence: 93%

“…As we turn on the external field h, we have a whole range of values where, before a critical value h = h c is reached, there is a magnetic order associated to spontaneous symmetry breaking [6], and the decoherence argument applies within the entire ordered phase. This means that, again, the only stable states are those that maximally break the Hamiltonian symmetry [7,8]. However, now the symmetry-breaking states are entangled, and their mixed-state reductions on arbitrary subsys-l A FIG.…”

Section: Introductionmentioning

confidence: 99%

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Mutual information and spontaneous symmetry breaking

2016

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We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions, and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g. at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly non trivial. We prove this result in general, by considering the quantum mutual information based on the $2-$R\'enyi entanglement entropy and using a locality result stemming from quasi-adiabatic continuation. Moreover, in the paradigmatic case of the exactly solvable one-dimensional quantum $XY$ model, we further verify the general result by considering also the quantum mutual information based on the von Neumann entanglement entropy

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Section: Comparison With Other Indicators Of Macroscopic Coherent Sup...mentioning

confidence: 90%

Section: On Products Of Pauli Matrices σ I Amentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Mutual information and spontaneous symmetry breaking

2016

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“…Not only. It is well known that, in the thermodynamic limit, the expectation value of an operator that commutes with the parity is the same if evaluated on |e {γ} or on |o {γ} [25,26,30]. We indicate such expectation value on one of the symmetric ground states as Ô{µi}…”

Section: A Quantitative Approach To the Distinguishabilitymentioning

confidence: 99%

“…On the other hand, the symmetric ground states, i.e. the ground states for which the order parameter is zero, are the ones for which both the concurrence below the factorization point [29,30] and the Von Neumann entropy [31] reach their maximum values.…”

Section: Introductionmentioning

confidence: 99%

Quench of a symmetry-broken ground state

Giampaolo¹,

Zonzo

2017

Phys. Rev. A

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We analyze the problem of how different ground states associated to the same set of the Hamiltonian parameters evolve after a sudden quench. To realize our analysis we define a quantitative approach to the local distinguishability between different ground states of a magnetically ordered phase in terms of the trace distance between the reduced density matrices obtained projecting two ground states in the same subset. Before the quench, regardless the particular choice of the subset, any system in a magnetically ordered phase is characterized by ground states that are locally distinguishable. On the other hand, after the quench, the maximum of the distinguishability shows an exponential decay in time. Hence, in the limit of very large time, all the informations about the particular initial ground state are lost even if the systems are integrable. We prove our claims in the framework of the magnetically ordered phases that characterize both the XY model and N -cluster Ising models. The fact that we find similar behavior in models within different classes of symmetry makes us confident about the generality of our results.

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Entanglement and quantum correlations in many-body systems: a unified approach via local unitary operations

Cianciaruso¹,

Giampaolo²,

Roga³

et al. 2014

Preprint

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Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum system. For pure states, the distance between a given state and its image under least-perturbing local unitary operations is a bona fide measure of quantum entanglement, the so-called entanglement of response, which can be extended to mixed states via the convex roof construction. On the other hand, when defined directly on mixed states perturbed by local unitary operations, such a distance turns out to be a bona fide measure of quantum correlations, the so-called discord of response. Exploiting this unified framework, we perform a detailed comparison between two-body entanglement and two-body quantum discord in infinite XY quantum spin chains both in symmetry-preserving and symmetry-breaking ground states as well as in thermal states at finite temperature. The results of the investigation show that in symmetry-preserving ground states the two-point quantum discord dominates over the two-point entanglement, while in symmetrybreaking ground states the two-point quantum discord is strongly suppressed and the two-point entanglement is essentially unchanged. In thermal states, for certain regimes of Hamiltonian parameters, we show that the pairwise quantum discord and the pairwise entanglement can increase with increasing thermal fluctuations.

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Classical nature of ordered phases: origin of spontaneous symmetry breaking

Cited by 3 publications

References 24 publications

Mutual information and spontaneous symmetry breaking

Mutual information and spontaneous symmetry breaking

Quench of a symmetry-broken ground state

Entanglement and quantum correlations in many-body systems: a unified approach via local unitary operations

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