Low-energy physics of isotropic spin-1 chains in the critical and Haldane phases

Binder, Moritz; Barthel, Thomas

doi:10.1103/physrevb.102.014447

Cited by 12 publications

(13 citation statements)

References 69 publications

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“…For larger system sizes, the support of the S ( 33)(k, ω) follows the two-soliton continuum of the Bethe-Ansatz. Also, the overall weight distribution agrees with the matrixproduct-state calculation presented in [39]. However, a detailed examination reveals that the one particle-hole excitations fail to reproduce the four-soliton excitations.…”

Section: Discussionsupporting

confidence: 76%

“…density) on the ground state [60,61]. Actually, since the dynamical structure factor of the SU(3) Heisenberg model consist of two-and multi-soliton continua [35,39,48,50], so we shall not expect the SMA to work in general. However, the two-soliton continuum narrows at small momenta, and the SMA allows to extract the velocity of the excitations.…”

Section: Single Mode Approximation and The Velocity Of Excitationsmentioning

confidence: 99%

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The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach

Vörös,

Penc

2021

Preprint

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We compute the dynamical spin structure factor S(k, ω) of the SU(3) Heisenberg chain variationally using a truncated Hilbert space spanned by the Gutzwiller projected particle-hole excitations of the Fermi sea, introduced in [B. Dalla Piazza et al., Nature Physics 11, 62 (2015)], with a modified importance sampling. We check the reliability of the method by comparing the S(k, ω) to exact diagonalization results for 18 sites and to the two-soliton continuum of the Bethe Ansatz for 72 sites. We get an excellent agreement in both cases. Detailed analysis of the finite-size effects shows that the method captures the critical Wess-Zumino-Witten SU(3)1 behavior and reproduces the correct exponent, with the exception of the size dependence of the weight of the bottom of the conformal tower. We also calculate the single-mode approximation for the SU(N ) Heisenberg model and determine the velocity of excitations. Finally, we apply the method to the SU(3) Haldane-Shastry model and find that the variational method gives the exact wave function for the lowest excitation at k = ±2π/3.

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Section: Discussionsupporting

confidence: 76%

Section: Single Mode Approximation and The Velocity Of Excitationsmentioning

confidence: 99%

The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach

Vörös,

Penc

2021

Preprint

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“…with Ŝi = ( Ŝ1 i , Ŝ2 i , Ŝ3 i ), ŜN+1 ≡ Ŝ1 , [ Ŝa i , Ŝb j ] = i δ i,j 3 c=1 abc Ŝc i , and ( Ŝi ) 2 = 2. The competition between the bilinear and biquadratic terms of the Hamiltonian (57) leads to a rich groundstate phase diagram, parametrized by the angle θ [60][61][62]. The model features a gapped dimerized phase (−3π/4 < θ < −π/4), the gapped Haldane phase (−π/4 < θ < π/4), an extended critical phase (π/4 < θ < π/2), and a gapless ferromagnetic (π/2 < θ < 5π/4).…”

Section: B Examples With or Without Optimizers In Non-closed Tns Setsmentioning

confidence: 99%

On the closedness and geometry of tensor network state sets

Barthel,

Lu,

Friesecke

2021

Preprint

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Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. We discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states (TTNS), and the multiscale entanglement renormalization ansatz (MERA) are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states (PEPS) are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

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“…Understanding the mechanism of such emergent phenomena in many-body systems involves methods and theories beyond the standard mean-field paradigm, which is the central but daunting task in various fields of condensed matter physics. In recent years, there has been proliferating amount of research on longrange entangled frustrated systems [9][10][11] and quantum many-body systems with topological order (TO) [12][13][14][15]. These systems feature strong interaction between local degrees of freedoms, whereby mean-field or single-mode approximations fail to capture the essential physics which requires theories beyond Landau's symmetry-breaking paradigm, such as Kitaev spin liquid [13] and Toric code (TC) model [12].…”

Section: Introductionmentioning

confidence: 99%

A statistical approach to topological entanglement: Boltzmann machine representation of higher-order irreducible correlation

Shi¹,

Kong²,

Trivedi³

2023

Preprint

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Higher-order correlation is an interesting phenomenon in many fields of physics and statistics. A quantum analogue of the higher-order correlation is the topological entanglement in topologically ordered states of matter at zero temperature, usually quantified by topological entanglement entropy (TEE). In this work, we propose a statistical interpretation that unifies the two under the same information-theoretic framework. We demonstrate that the existence of a non-zero TEE can be understood in the statistical view as the emergent nth order mutual information In (for arbitrary integer n ≥ 3) reflected in projectively measured samples, which also makes explicit the equivalence between the two existing methods for its extraction -the Kitaev-Preskill and the Levin-Wen construction. To exploit the statistical nature of In, we construct a restricted Boltzmann machine (RBM) which captures the higher-order correlation and/or topological entanglement that are encoded in the distribution of projected sample by representing the entanglement Hamiltonian of a local region under the proper basis. Furthermore, we derive a closed form which presents a method to interrogate the trained RBM, making explicit the analytical form of arbitrary order of correlation relevant for In in terms of the entanglement Hamiltonian. We remark that the interrogation method for extracting higher-order correlation can also be applied in the construction of auxiliary fields which disentangle many-body interactions relevant for diverse interacting models.

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Low-energy physics of isotropic spin-1 chains in the critical and Haldane phases

Cited by 12 publications

References 69 publications

The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach

The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach

On the closedness and geometry of tensor network state sets

A statistical approach to topological entanglement: Boltzmann machine representation of higher-order irreducible correlation

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