Open XXZ chain and boundary modes at zero temperature

Grijalva, Sebastián; Nardis, Jacopo De; Terras, V.

doi:10.21468/scipostphys.7.2.023

Cited by 12 publications

(24 citation statements)

References 61 publications

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“…We show that for certain boundary conditions, those which break the time reversal invariance of the bulk, the model supports bound states at the boundaries. These boundary bound states, while * crylands@umd.edu being exact eigenstates of the system do not correspond to solutions of the Bethe Ansatz equations which marks them as distinct from boundary modes previously studied via Bethe Ansatz [16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 92%

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Exact boundary modes in an interacting quantum wire

Rylands

2020

Phys. Rev. B

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The boundary modes of one dimensional quantum systems can play host to a variety of remarkable phenomena. They can be used to describe the physics of impurities in higher dimensional systems, such as the ubiquitous Kondo effect or can support Majorana bound states which play a crucial role in the realm of quantum computation. In this work we examine the boundary modes in an interacting quantum wire with a proximity induced pairing term. We solve the system exactly by Bethe Ansatz and show that for certain boundary conditions the spectrum contains bound states localized about either edge. The model is shown to exhibit a first order phase transition as a function of the interaction strength such that for attractive interactions the ground state has bound states at both ends of the wire while for repulsive interactions they are absent. In addition we see that the bound state energy lies within the gap for all values of the interaction strength but undergoes a sharp avoided level crossing for sufficiently strong interaction, thereby preventing its decay. This avoided crossing is shown to occur as a consequence of an exact self-duality which is present in the model.

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Section: Introductionmentioning

confidence: 92%

“…We consider only positive values of θ j , µ α and furthermore all rapidities and Bethe parameters must be distinct, θ j = θ k , µ α = µ β and non zero otherwise the corresponding wavefunction vanishes [41,47]. The set of equations given in (23) and (24) are the Bethe Ansatz equations.…”

Section: Bethe Ansatz Equationsmentioning

confidence: 99%

Exact boundary modes in an interacting quantum wire

Rylands

2020

Phys. Rev. B

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“…We will denote such a boundary root by λ+ in the former case and by λ− in the latter case. The presence of such a boundary root within the set of roots for the ground state depends on both boundary parameters ς and on the parity of the number of sites N of the chain (see [131]). We refer to [131] for a detailed study of the set of Bethe roots describing the ground state, and in particular of the cases in which it contains such a boundary root, in the regime ∆ > 1.…”

Section: Expression Of the Correlation Functions In The Half-infinite...mentioning

confidence: 99%

“…is due to the fact that, in that case, the boundary root approaches a double pole of the Bethe equation, which corresponds to a doubling of the same term in (5.38), see [131].…”

Section: Expression Of the Correlation Functions In The Half-infinite...mentioning

confidence: 99%

“…Instead, for long enough chains, we expect the influence of the boundary field at the other side of the chain to be only indirect (i.e. mainly encoded in the structure of the ground state and not in the explicit expression of the correlation functions themselves, see [131]). This type of physical argument motivates us to initiate our study by considering some special choice of the boundary magnetic field at site N .…”

Section: Introductionmentioning

confidence: 99%

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Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields

Niccoli,

Terras

2022

Preprint

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In this paper we continue our derivation of the correlation functions of open quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time for the more involved case of the XXZ spin 1/2 chains. We develop our study in the framework of the quantum Separation of Variables (SoV), which gives us both the complete spectrum characterization and simple scalar product formulae for separate states, including transfer matrix eigenstates. Here, we leave the boundary magnetic field in the first site of the chain completely arbitrary, and we fix the boundary field in the last site N of the chain to be a specific value along the zdirection. This is a natural first choice for the unparallel boundary magnetic fields. We prove that under these special boundary conditions, on the one side, we have a simple enough complete spectrum description in terms of homogeneous Baxter like T Q-equation. On the other side, we prove a simple enough description of the action of a basis of local operators on transfer matrix eigenstates as linear combinations of separate states. Thanks to these results, we achieve our main goal to derive correlation functions for a set of local operators both for the finite and half-infinite chains, with multiple integral formulae in this last case. B On the boundary-bulk decompositionB.1 Construction of an A − (λ|α, β − 1) and D − (λ|α, β + 1

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Bethe ansatz approach for dissipation: exact solutions of quantum many-body dynamics under loss

et al. 2020

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We develop a Bethe ansatz based approach to study dissipative systems experiencing loss. The method allows us to exactly calculate the spectra of interacting, many-body Liouvillians. We discuss how the dissipative Bethe ansatz opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.

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Open XXZ chain and boundary modes at zero temperature

Cited by 12 publications

References 61 publications

Exact boundary modes in an interacting quantum wire

Exact boundary modes in an interacting quantum wire

Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields

Bethe ansatz approach for dissipation: exact solutions of quantum many-body dynamics under loss

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