Spinon confinement and deconfinement in spin-1 chains

Vanderstraeten, Laurens; Wybo, Elisabeth; Chepiga, Natalia; Verstraete, Frank; Mila, Frédéric

doi:10.1103/physrevb.101.115138

Cited by 16 publications

(10 citation statements)

References 68 publications

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“…This mechanism is known as string breaking and has been investigated extensively from a static point of view [ 4 – 11 ] while recently also its dynamics has gained increased attention [ 12 – 25 ]. Importantly, many aspects of confinement cannot only be realized in gauge theories, but also in conventional quantum spin chains [ 26 – 45 ]. Yet, it has remained an open question whether quantum spin models can inherit also the fundamental dynamical process of string breaking.…”

Section: Introductionmentioning

confidence: 99%

Real-time dynamics of string breaking in quantum spin chains

et al. 2020

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String breaking is a central dynamical process in theories featuring confinement, where a string connecting two charges decays at the expense of the creation of new particle-antiparticle pairs. Here, we show that this process can also be observed in quantum Ising chains where domain walls get confined either by a symmetry-breaking field or by long-range interactions. We find that string breaking occurs, in general, as a two-stage process. First, the initial charges remain essentially static and stable. The connecting string, however, can become a dynamical object. We develop an effective description of this motion, which we find is strongly constrained. In the second stage, which can be severely delayed due to these dynamical constraints, the string finally breaks. We observe that the associated timescale can depend crucially on the initial separation between domain walls and can grow by orders of magnitude by changing the distance by just a few lattice sites. We discuss how our results generalize to one-dimensional confining gauge theories and how they can be made accessible in quantum simulator experiments such as Rydberg atoms or trapped ions.

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Section: Introductionmentioning

confidence: 99%

Real-time dynamics of string breaking in quantum spin chains

et al. 2020

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“…When a (even very small) longitudinal field is introduced, an effective attractive potential is generated and the domain walls get confined in bound states whose nature is very similar to the mesons of QCD. Following the pioneering work by McCoy and Wu, confinement has then been found and investigated with various analytical and numerical methods in thermal equilibrium in several quantum one-dimensional models [3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Confinement in the spectrum of a Heisenberg–Ising spin ladder

Lagnese¹,

Surace²,

Kormos³

et al. 2020

J. Stat. Mech.

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We consider the quantum quench dynamics of a Heisenberg-Ising spin ladder which is an archetypal model in which confinement of elementary excitations is triggered by internal interactions rather than an external field. We show that the confinement strongly affects the light cone structure of correlation functions providing signatures of the velocities of the mesons of the model. We also show that the meson masses can be measured from the real time analysis of the evolution of the order parameter.

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“…In the case of kinks, as depicted here, the two virtual legs of B tensors need to be identical and thus carry the same representations, and it follows automatically that physical symmetry sector of the kink states needs to be a spinor representation. These constructions are well-known in the case of half-integer spin chains [92], where they also correspond to the renowned result that the elementary excitations in e.g. the half-integer spin Heisenberg chain are spinors [93,94].…”

Section: Jhep07(2021)207mentioning

confidence: 66%

Lattice regularisation and entanglement structure of the Gross-Neveu model

Roose

Bultinck

Vanderstraeten

et al. 2021

J. High Energ. Phys.

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We construct a Hamiltonian lattice regularisation of the N-flavour Gross-Neveu model that manifestly respects the full O(2N) symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorems. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementary kink excitations. We show that our Hamiltonian model can be solved analytically in the large N limit, producing the correct expression for the mass gap. Furthermore, we perform extensive numerical matrix product state simulations for N = 2, thereby recovering the emergent Lorentz symmetry and the proper non-perturbative mass gap scaling in the continuum limit. Finally, our simulations also reveal how the continuum limit manifests itself in the entanglement spectrum. As expected from conformal field theory we find two conformal towers, one tower spanned by the linear representations of O(4), corresponding to the trivial phase, and the other by the projective (i.e. spinor) representations, corresponding to the SPT phase.

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Spinon confinement and deconfinement in spin-1 chains

Cited by 16 publications

References 68 publications

Real-time dynamics of string breaking in quantum spin chains

Real-time dynamics of string breaking in quantum spin chains

Confinement in the spectrum of a Heisenberg–Ising spin ladder

Lattice regularisation and entanglement structure of the Gross-Neveu model

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