Phantom Bethe roots in the integrable open spin-
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 XXZ chain

Zhang, Xin; Klümper, Andreas; Popkov, Vladislav

doi:10.1103/physrevb.103.115435

Cited by 15 publications

(33 citation statements)

References 21 publications

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“…We like to note that (16) holds literally for case n = n + . For n = n − the +E 0 contribution in ( 16) is to be replaced by −E 0 , see [28]. We find that the BAE (18) for…”

mentioning

confidence: 87%

“…and +(−) corresponds to the right (left) field. The Bethe roots µ j satisfy BAE of a somewhat bulky form [25][26][27][28]. After some algebra [28] we find that if…”

mentioning

confidence: 99%

“…. , N − 1, each set of N Bethe roots contains n phantom Bethe roots of type (11), where n takes one of two values n + = N − M and n − = M + 1 [28,29]. The remaining N − n Bethe roots x j (= µ n+j ) are regular and satisfy reduced BAE…”

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confidence: 99%

“…Bethe states, while the remaining 2 N − dim G + M eigenstates are contained in the other, complementary BAE set for n = M + 1 [28,29]. Unlike in the periodic setup, where some Bethe eigenstates contain PBR modes, and other eigenstates are fully regular, in open systems, satisfying criterion ( 17), all 2 N eigenstates include phantom Bethe roots.…”

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confidence: 99%

“…We demonstrate that such "phantom" Bethe states are spin-helix states (4) with appropriately chosen parameters. The phantom Bethe states for mixtures of phantom and regular Bethe roots can be also obtained explicitly and show chiral features [28,29].…”

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confidence: 99%

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Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains

2021

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We demonstrate the existence of a special chiral "phantom" mode with some analogy to a Goldstone mode in the anisotropic quantum XXZ Heisenberg spin chain. The phantom excitations contribute zero energy to the eigenstate, but a finite fixed quantum of momentum k0. The mode exists not due to symmetry principles, but results from non-trivial scattering properties of magnons with momentum k0 given by the anisotropy via cos k0 = ∆. Different occupations of the phantom mode lead to energetical degeneracies between different magnetization sectors in the periodic case. This mode originates from special string-type solutions of the Bethe ansatz equations with unbounded rapidities, the phantom Bethe roots (PBR). We derive criteria under which the spectrum contains eigenstates with PBR, both in open and periodically closed integrable systems, for spin 1/2 and higher spins, and discuss the respective chiral eigenstates. The simplest of such eigenstates, the spin helix state which is a periodically modulated state of chiral nature, is built up from the phantom excitations exclusively. Implications of our results for experiments are discussed.

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“…We like to note that (16) holds literally for case n = n + . For n = n − the +E 0 contribution in ( 16) is to be replaced by −E 0 , see [28]. We find that the BAE (18) for…”

mentioning

confidence: 87%

“…and +(−) corresponds to the right (left) field. The Bethe roots µ j satisfy BAE of a somewhat bulky form [25][26][27][28]. After some algebra [28] we find that if…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains

2021

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Unveiling chiral states in the XXZ chain: finite-size scaling probing symmetry-enriched c = 1 conformal field theories

Wei,

Mkhitaryan,

Sedrakyan

2024

J. High Energ. Phys.

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We study the low-energy properties of the one-dimensional spin-1/2 XXZ chain with time-reversal symmetry-breaking pseudo-scalar chiral interaction and propose a phase diagram for the model. In the integrable case of the isotropic Heisenberg model with the chiral interaction, we employ the thermodynamic Bethe ansatz to find “chiralization”, the response of the ground state versus the strength of the pseudo-scalar chiral interaction of a chiral Heisenberg chain. Unlike the magnetization case, the chirality of the ground state remains zero until the transition point corresponding to critical coupling αc = 2J/π with J being the antiferromagnetic spin-exchange interaction. The central-charge c = 1 conformal field theories (CFTs) describe the two phases with zero and finite chirality. We show for this particular case and conjecture more generally for similar phase transitions that the difference between two emergent CFTs with identical central charges lies in the symmetry of their ground state (lightest weight) primary fields, i.e., the two phases are symmetry-enriched CFTs. At finite but small temperatures, the non-chiral Heisenberg phase acquires a finite chirality that scales with the temperature quadratically. We show that the finite-size effect around the transition point probes the transition.

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Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin−12 chain

2021

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Phantom Bethe roots in the integrable open spin- 12 XXZ chain

Cited by 15 publications

References 21 publications

Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains

Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains

Unveiling chiral states in the XXZ chain: finite-size scaling probing symmetry-enriched c = 1 conformal field theories

Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin−12 chain

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