Frustrated transverse-field Ising model

Oitmaa, J.

doi:10.1088/1751-8121/ab63e6

Cited by 13 publications

(7 citation statements)

References 15 publications

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“…The stripe-PM quantum transition seems to dis- play a tricritical point separating a first-order transition line from a second-order transition line -similarly to the classical case [52]. Interestingly, the position of the quantum tricritical point seems to be closer to the degeneracy point than the classical tricritical point [52,53], i.e. (J 2 /J 1 ) q < (J 2 /J 1 ) cl ≈ 0.67, as illustrated schematically in Fig.…”

Section: The Transverse-field J1-j2 Ising Modelmentioning

confidence: 82%

“…The quantum phase diagram (T = 0) of the model remains widely debated, although some properties seem to be consistent across different methods [49][50][51][52][53]. In Fig.…”

Section: The Transverse-field J1-j2 Ising Modelmentioning

confidence: 95%

“…50 reported the onset of a string valence-bond solid for finite transverse fields. The quantum phase transition from the Néel to the PM state is believed to be second-order and in the 3D Ising universality class [53] -although some methods report a regime of first-order transition near J 2 /J 1 = 1/2 [51]. The stripe-PM quantum transition seems to dis- play a tricritical point separating a first-order transition line from a second-order transition line -similarly to the classical case [52].…”

Section: The Transverse-field J1-j2 Ising Modelmentioning

confidence: 99%

“…This model has been studied extensively in the recent literature [48][49][50][51][52][53], and here we give a brief overview of the proposed phase diagrams of the frustrated case, where J 2 > 0. Because the model is invariant upon changing the signs of J 1 or h, hereafter we focus on the case of J 1 , h > 0.…”

Section: The Transverse-field J1-j2 Ising Modelmentioning

confidence: 99%

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Strong-coupling expansion of multi-band interacting models: mapping onto the transverse-field $J_1$-$J_2$ Ising model

Wang,

Christensen,

Berg

et al. 2021

Preprint

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We investigate a class of two-dimensional two-band microscopic models in which the inter-band repulsive interactions play the dominant role. We first demonstrate three different schemes of constraining the ratios between the three types of inter-band interactions -density-density, spin exchange, and pair-hopping -that render the model free of the fermionic sign-problem for any filling and, consequently, amenable to efficient Quantum Monte Carlo simulations. We then study the behavior of these sign-problem-free models in the strong-coupling regime. In the cases where spin-rotational invariance is preserved or lowered to a planar symmetry, the strong-coupling ground state is a quantum paramagnet. However, in the case where there is only a residual Ising symmetry, the strong-coupling expansion maps onto the transverse-field J1-J2 Ising model, whose pseudospins are associated with local inter-band magnetic order. We show that by varying the band structure parameters within a reasonable range of values, a variety of ground states and quantum critical points can be accessed in the strong-coupling regime, some of which are not realized in the weakcoupling regime. We compare these results with the case of the single-band Hubbard model, where only intra-band repulsion is present, and whose strong-coupling behavior is captured by a simple Heisenberg model.

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Section: The Transverse-field J1-j2 Ising Modelmentioning

confidence: 82%

“…The quantum phase diagram (T = 0) of the model remains widely debated, although some properties seem to be consistent across different methods [49][50][51][52][53]. In Fig.…”

Section: The Transverse-field J1-j2 Ising Modelmentioning

confidence: 95%

Section: The Transverse-field J1-j2 Ising Modelmentioning

confidence: 99%

Section: The Transverse-field J1-j2 Ising Modelmentioning

confidence: 99%

See 2 more Smart Citations

Strong-coupling expansion of multi-band interacting models: mapping onto the transverse-field $J_1$-$J_2$ Ising model

Wang,

Christensen,

Berg

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Although graph decomposition methods have been employed already decades ago in order to obtain high-order series expansions of many-body systems [1][2][3][4][5], they continue to be a state of the art approach to perform calculations for quantum lattice models, for example using perturbative methods like high-temperature series expansions [6,7], Rayleigh-Schrödinger perturbation theory [8][9][10], perturbative continuous unitary transformations (pCUTs) [11][12][13][14][15][16] or non-perturbative numerical tools like exact diagonalization [17][18][19], density matrix renormalization group [20], and graph-based continuous unitary transformations [21][22][23] in the context of numerical linked cluster expansions. Historically the graph decomposition methods for high-order series expansions were exclusively applicable to extensive quantities like ground-state energies [1,2] or had to take into account also disconnected graphs [3,24].…”

Section: Introductionmentioning

confidence: 99%

Linked Cluster Expansions via Hypergraph Decompositions

Mühlhauser,

Schmidt

2022

Preprint

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We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into equivalence classes essentially governed by hypergraph isomorphism. Concretely, a reduced König representation of the hypergraphs is used to make the equivalence relation accessible by graph isomorphism. During this procedure we determine the embedding factor for each equivalence class, which is used in the final resummation in order to obtain the final result. As an instructive example we calculate the ground-state energy and a particular excitation gap of the plaquette Ising model in a transverse field on the three-dimensional cubic lattice.

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Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

Fazza

Sulejmanpašić

2023

J. High Energ. Phys.

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We construct Villain Hamiltonians for compact scalars and abelian gauge theories. The Villain integers are promoted to integral spectrum operators, whose canonical conjugates are naturally compact scalars. Further, depending on the theory, these conjugate operators can be interpreted as (higher-form) gauge fields. If a gauge symmetry is imposed on these dual gauge fields, a natural constraint on the Villain operator leads to the absence of defects (e.g. vortices, monopoles,…). These lattice models therefore have the same symmetry and anomaly structure as their corresponding continuum models. Moreover they can be formulated in a way that makes the well-know dualities look manifest, e.g. a compact scalar in 2d has a T-duality, in 3d is dual to a U(1) gauge theory, etc. We further discuss the gauged version of compact scalars on the lattice, its anomalies and solution, as well as a particular limit of the gauged XY model at strong coupling which reduces to the transverse-field Ising model. The construction for higher-form gauge theories is similar. We apply these ideas to the constructions of some models which are of interest to fracton physics, in particular the XY-plaquette model and the tensor gauge field model. The XY-plaquette model in 2+1d coupled to a tensor gauge fields at strong gauge coupling is also exactly described by a transverse field quantum J1 − J2 Ising model with J1 = 2J2, and discuss the phase structure of such models.

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Frustrated transverse-field Ising model

Cited by 13 publications

References 15 publications

Strong-coupling expansion of multi-band interacting models: mapping onto the transverse-field $J_1$-$J_2$ Ising model

Strong-coupling expansion of multi-band interacting models: mapping onto the transverse-field $J_1$-$J_2$ Ising model

Linked Cluster Expansions via Hypergraph Decompositions

Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities

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