Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains

Wang, Lihua; Chung, S. G.

doi:10.1143/jpsj.81.114712

Cited by 6 publications

(9 citation statements)

References 45 publications

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“…In exact agreement with Bethe ansatz GS energy [31], this allows for precise computation of spin-spin correlations for separations over 10000 sites. The correlations reproduced results in ref [32], both of which agree with the prediction by the conformal field theory [33] that there is a loga- rithmic correction multiplicative to the power-law decay predicted by the bosonization theory [34]. As Fig.…”

supporting

confidence: 87%

Gapless and Massive 1D Singlet Dispersion Channel in Infinite Spin-1/2 Ladders ---Infinite Quasi-1D Entanglement Perturbation Theory for Excitation

Wang,

Parvej,

Yang

et al. 2020

Preprint

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We solve for the elementary excitation in infinite quasi-1D quantum lattices by extending the recently developed infinite quasi-1D entanglement perturbation theory. The wave function of an excited state is variationally determined by optimizing superposition of cluster operation, each of which is composed of simultaneous on-site operation inside a block of lattice sites, on the ground state in a form of plane wave. The excitation energy with respect to the wave number gives the spectra for an elementary excitation. Our method is artificial broadening free and is adaptive for various quasiparticle pictures. Using the triplet spectrum, the application to ∞-by-N antiferromagnetic spin-1 2 ladders for N = 2, 4, 6, 8, and 10 confirms a previous report that there is a quantum dimensional transition, namely, the lattice transits from quasi-1D to 2D at a finite critical value Nc = 10. The massless triplet dispersion at (π, π) sees a vanishing gap. Our results detect the anomaly at (π, 0) in the triplet spectrum, agreeing well with the inelastic neutron scattering measurement of a macroscopic sample. Surprisingly, our results also reveal a gapless and massive 1D singlet dispersion channel that is much lower than the triplet excitation. We note, however, the dimensional transition is determined by the massless triplet dispersion.

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confidence: 87%

Gapless and Massive 1D Singlet Dispersion Channel in Infinite Spin-1/2 Ladders ---Infinite Quasi-1D Entanglement Perturbation Theory for Excitation

Wang,

Parvej,

Yang

et al. 2020

Preprint

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“…6b, which shows that the single CSF results mimic the exact result even for large lattice sizes. However, the shortrange behavior of the exact spin-spin correlation function follows a power law decay [39], Ŝz Using the method of generating functions, Sato et al [163] found the exact thermodynamic limit results for S z 1 • S z r up to r = 7, which are shown in Table III along [164], derived a relation of A(r) = −0.1473r −0.9604 with an error of 0.1% for the odd separations, which also fits the even sites with an opposite sign. Based on a bosonization approach, Hikihara and Furusaki [165] find a critial exponent b = −1.…”

Section: Spin-spin Correlation Functionsmentioning

confidence: 99%

Combined unitary and symmetric group approach applied to low-dimensional spin systems

Dobrautz,

Katukuri,

Bogdanov

et al. 2021

Preprint

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A novel combined unitary and symmetric group approach is used to study the spin-1 2 Heisenberg model and related Fermionic systems in a spin-adapted representation, using a linearlyparameterised Ansatz for the many-body wave function. We show that a more compact ground state wave function representation is obtained when combining the symmetric group, Sn, in the form of permutations of the underlying lattice site ordering, with the cumulative spin-coupling based on the unitary group, U(n). In one-dimensional systems the observed compression of the wave function is reminiscent of block-spin renormalization group approaches, and allows us to study larger lattices (here taken up to 80 sites) with the spin-adapted full configuration interaction quantum Monte Carlo method, which benefits from the sparsity of the Hamiltonian matrix and the corresponding sampled eigenstates that emerge from the reordering. We find that in an optimal lattice ordering the configuration state function with highest weight already captures with high accuracy the spin-spin correlation function of the exact ground state wave function. This feature is found for more general lattice models, such as the Hubbard model, and ab initio quantum chemical models, in this work exemplified by a one-dimensional hydrogen chain. We also provide numerical evidence that the optimal lattice ordering for the unitary group approach is not generally equivalent to the optimal ordering obtained for methods based on matrix-product states, such as the density-matrix renormalization group approach.

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“…For instance, DMRG works extremely well in 1D but not in 2D. When dealing with a 2D lattice, the wave function obtained in DMRG has a matrix product state (MPS) [22,[38][39][40][41][42][43][44][45][46] form that is built on a winded 1D lattice which resembles the 2D lattice [15,36]. See Fig.2(b) for an illustration.…”

Section: A Problem Descriptionmentioning

confidence: 99%

Signature of a quantum dimensional transition in the spin- 12 antiferromagnetic Heisenberg model on a square lattice and space reduction in the matrix product state

Wang

Kim

2019

Phys. Rev. B

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We study the spin-1 2 antiferromagnetic Heisenberg model on an infinity-by-N square lattice for even N 's up to 14. Previously, the nonlinear sigma model perturbatively predicts that its spin rotational symmetry asymptotically breaks when N → ∞, i.e., when it is two-dimensional (2D). However, we identified a critical width Nc = 10 for which this symmetry breaks spontaneously. It defines a dimensional transition from one-dimension (1D) including quasi-1D to 2D. The finite-size effect differs from that of the N -by-N lattice. The ground state (GS) energy per site approaches the thermodynamic limit value, in agreement with the previously accepted value, by one order of 1/N faster than when using N -by-N lattices in the literature. We build and variationally solve a matrix product state (MPS) on a chain, converting the N sites in the rung into an effective site. We show that the area law of entanglement entropy does not apply when N increases in our method, and show that the reduced density matrix of each effective site will have a saturating number of dominant diagonal elements with increasing N . These two characteristics make the MPS rank needed to obtain a demanded energy accuracy quickly saturate when N is large, making our algorithm efficient for large N 's. And, the latter enables space reduction in MPS. Within the framework of MPS, we prove a theorem that the spin-spin correlation at infinite separation is the square of staggered magnetization and demonstrate that the eigenvalue structure of a building MPS unit of g | g , | g being the GS, is responsible for order, disorder and quasi-long-range order.

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Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains

Cited by 6 publications

References 45 publications

Gapless and Massive 1D Singlet Dispersion Channel in Infinite Spin-1/2 Ladders ---Infinite Quasi-1D Entanglement Perturbation Theory for Excitation

Gapless and Massive 1D Singlet Dispersion Channel in Infinite Spin-1/2 Ladders ---Infinite Quasi-1D Entanglement Perturbation Theory for Excitation

Combined unitary and symmetric group approach applied to low-dimensional spin systems

Signature of a quantum dimensional transition in the spin- 12 antiferromagnetic Heisenberg model on a square lattice and space reduction in the matrix product state

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