Heisenberg necklace model in a magnetic field

Tsvelik, A. M.; Zaliznyak, Igor

doi:10.1103/physrevb.94.075152

Cited by 19 publications

(34 citation statements)

References 33 publications

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“…Similar calculations have been previously done by Tsvelik. 19,27 There are three currents to study when considering the Kondo-Heisenberg model. A U (1) 2 current describing the charge degrees of freedom of the 1DEG, a SU (2) 1 current describing the spin degrees of freedom of the 1DEG, and a second SU (2) 1 current describing the Heisenberg spins, leading to a total current structure of U (1) 2 × SU (2) 1 × SU (2) 1 , as shown in Eq.…”

Section: Previously Proposed Majorana Zero Modesmentioning

confidence: 99%

Topology and the one-dimensional Kondo-Heisenberg model

et al. 2020

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The Kondo-Heinsberg chain is an interesting model of a strongly correlated system which has a broad superconducting state with pair-density wave (PDW) order. Some of us have recently proposed that this PDW state is a symmetry-protected topological (SPT) state, and the gapped spin sector of the model supports Majorana zero modes. In this work, we reexamine this problem using a combination of numeric and analytic methods. In extensive density matrix renormalization group calculations, we find no evidence of a topological ground state degeneracy or the previously proposed Majorana zero modes in the PDW phase of this model. This result motivated us to reexamine the original arguments for the existence of the Majorana zero modes. A careful analysis of the effective continuum field theory of the model shows that the Hilbert space of the spin sector of the theory does not contain any single Majorana fermion excitations. This analysis shows that the PDW state of the doped 1D Kondo-Heisenberg model is not an SPT with Majorana zero modes. arXiv:2002.01483v1 [cond-mat.str-el]

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Section: Previously Proposed Majorana Zero Modesmentioning

confidence: 99%

Topology and the one-dimensional Kondo-Heisenberg model

et al. 2020

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“…We have argued in the first section that the modified truncated loop model could be formulated as a model with Osp(2|2) symmetry. We see in fact that it is also possible to formulate it as a model with more symmetry, namely U q so (5). As observed in other polymer problems (see, e.g., the dilute self-avoiding walks on the hexagonal lattice), the presence of this extra quantum group symmetry does not seem to be simply related with features of the continuum limit [29].…”

Section: From the Dilute Two Color Model To Bmentioning

confidence: 64%

“…A lasting mystery is the value of the thermal exponent ν. It has been suggested [5] that the corresponding dimension might be obtained by putting p = 2, s = 0 in (112), leading to…”

Section: Comparison With Expected Properties In the Untruncated Casementioning

confidence: 99%

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On truncations of the Chalker-Coddington model

et al. 2019

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The supersymmetric reformulation of physical observables in the Chalker-Coddington model (CC) for the plateau transition in the integer quantum Hall effect leads to a reformulation of its critical properties in terms of a 2D non-compact loop model or a 1D non-compact gl(2|2) spin chain. Following a proposal by Ikhlef, Fendley and Cardy [11], we define and study a series of truncations of these loop models and spin chains, involving a finite and growing number of degrees of freedom per site. The case of the first truncation is solved analytically using the Bethe-ansatz. It is shown to exhibit many of the qualitative features expected for the untruncated theory, including a quadratic spectrum of exponents with a continuous component, and a normalizable ground state below that continuum. Quantitative properties are however at odds with the results of simulations on the CC model. Higher truncations are studied only numerically. While their properties are found to get closer to those of the CC model, it is not clear whether this is a genuine effect, or the result of strong finite-size corrections.

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“…The goal of this paper is to demonstrate that this uncertainty can be removed by realizing CLS in KondoHeisenberg systems (KHS) [39][40][41][42][43] which consist of localized spins and itinerant electrons. Their coexistence leads to a competition between the direct Heisenberg spin ex-change and the RKKY interaction generated by the electrons, see Fig.1.…”

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confidence: 99%

Chiral Spin Order in Kondo-Heisenberg Systems

Tsvelik

Yevtushenko

2017

Phys. Rev. Lett.

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We demonstrate that Kondo-Heisenberg systems, consisting of itinerant electrons and localized magnetic moments (Kondo impurities), can be used as a principally new platform to realize scalar chiral spin order. The underlying physics is governed by a competition of the Ruderman-KittelKosuya-Yosida (RKKY) indirect exchange interaction between the local moments with the direct Heisenberg one. When the direct exchange is weak and RKKY dominates the isotropic system is in the disordered phase. A moderately large direct exchange leads to an Ising-type phase transition to the phase with chiral spin order. Our finding paves the way towards pioneering experimental realizations of the chiral spin liquid in low dimensional systems with spontaneously broken time reversal symmetry.PACS numbers: 75.30. Hx, 71.10.Pm, 72.15.Nj Interactions between magnetic moments usually lead to some kind of magnetic order where rotational symmetry is broken and the order parameter is linear in spins [1]. This is what happens in ferromagnets, antiferromagnets and all sorts of helimagnets. Villain has demonstrated [2] that, in addition to the magnetic order, helical magnets possess a vector chiral order parameter. It is bilinear in spins and is related to the mutual orientation of neighboring spins. This chiral order breaks the discrete symmetry and can exist even without the magnetic order [3]. The discovery of the vector chiral order has given rise to the idea that there could exist an order which includes a combination of three spins. The corresponding order parameter is a mixed product of three neighboring spins, see O c in Eq.(1) below and Refs. [4,5]. It breaks time-reversal and parity symmetries. Such a local order parameter is considered as the key quantity for description of exotic magnetic phases [4]. In contemporary language, O c is referred to as "scalar chiral spin order" and the state of matter with (spontaneously) broken time-reversal and parity symmetries but with conserved spin rotational symmetry is called Chiral Spin Liquid (CSL) [6]. The seminal example possessing the CSL symmetry is the Kalmeyer-Laughlin model [7][8][9][10]. Its wave functions demonstrate the topological behavior inherent in the fractional quantum Hall effect. Thus, the Kalmeyer-Laughlin model links spin liquids and topologically nontrivial states [11][12][13][14][15][16] and can be called "topological CSL". An increasing interest in the topological CSL [17][18][19][20][21][22][23] has been stimulated, in part, by a search for exotic (anyon) superconductivity [24,25] and by the physics of skyrmions [26][27][28][29]. The latter can be realized in magnets with the chirality resulting either from the lattice structure or from the Dzyaloshinskii-Moriya interaction [30][31][32][33].Although the concept of CSL and its order parameter O c were introduced in the 80-ties, it still remains unclear (color on-line) Competition between two different spin interactions in KHS: The spin on each lattice site is decomposed in terms of an orthonormal triad e1,2,3 (green ar...

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Heisenberg necklace model in a magnetic field

Cited by 19 publications

References 33 publications

Topology and the one-dimensional Kondo-Heisenberg model

Topology and the one-dimensional Kondo-Heisenberg model

On truncations of the Chalker-Coddington model

Chiral Spin Order in Kondo-Heisenberg Systems

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