Phase diagram of the frustrated J 1 − J 2 transverse field Ising model on the square lattice

Sadrzadeh, M.; Langari, A.

doi:10.1088/1742-6596/969/1/012114

Cited by 4 publications

(4 citation statements)

References 18 publications

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“…In the case of Ising model on CL, quantum fluctuations introduced by both transverse magnetic field [16,17] and in-plane XY interactions [18][19][20][21] lift the classical degeneracy of the highly frustrated point J 2 = J 1 toward a nonmagnetic plaquette-VBS phase [16][17][18]22] with broken translational symmetry, which shows two-fold degeneracy. The plaquette-VBS phase, which is mediated by anharmonic quantum fluctuations as an order-by-disorder phenomenon [23][24][25], emerges from an exponentially degenerate classical background, which can not be observed within linear spin-wave theory [26,27] due to strong frus-tration. In order to shed more light on the highly frustrated region, in the first part of our paper, we obtain the GS phase diagram of CL accurately by using a variational tree tensor-network (TTN) ansatz and compare it with previous studies.…”

Section: Introductionmentioning

confidence: 99%

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

2019

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We investigate the ground-state phase diagram of the frustrated transverse field Ising (TFI) model on the checkerboard lattice (CL), which consists of Néel, collinear, quantum paramagnet and plaquette-valence bond solid (VBS) phases. We implement a numerical simulation that is based on the recently developed unconstrained tree tensor network (TTN) ansatz, which systematically improves the accuracy over the conventional methods as it exploits the internal gauge selections. At the highly frustrated region (J2 = J1), we observe a second order phase transition from plaquette-VBS state to paramagnet phase at the critical magnetic field, Γc = 0.28, with the associated critical exponents ν = 1 and γ ≃ 0.4, which are obtained within the finite size scaling analysis on different lattice sizes N = 4 × 4, 6 × 6, 8 × 8. The stability of plaquette-VBS phase at low magnetic fields is examined by spin-spin correlation function, which verifies the presence of plaquette-VBS at J2 = J1 and rules out the existence of a Néel phase. In addition, our numerical results suggest that the transition from Néel (for J2 < J1) to plaquette-VBS phase is a deconfined phase transition. Moreover, we introduce a mapping, which renders the low-energy effective theory of TFI on CL to be the same model on J1 − J2 square lattice (SL). We show that the plaquette-VBS phase of the highly frustrated point J2 = J1 on CL is mapped to the emergent string-VBS phase on SL at J2 = 0.5J1.

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Section: Introductionmentioning

confidence: 99%

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

2019

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“…This model is sometimes called the transverse field J 1 − J 2 Ising model. The phase diagram of such models has been studied in 13 [30][31][32][33].…”

Section: 29)mentioning

confidence: 99%

“…is then to assume that there is one phase transition and that in the low field phase we have exponential number of degenerate ground states. The nature of the transition is not clear (see [31,[33][34][35]). In [34] a transition at the value h/J 1 ≈ 0.5, which translates to J ≈ √ 2 ≈ 1.41.…”

Section: 29)mentioning

confidence: 99%

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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“…Nevertheless, even the value of R * in the latter cases has been a subject of controversy with rather different estimates ranging from the early −1.1 [9] down to the latest −0.67 [16]. The effects of a transverse field [19][20][21] and stacking of the 2D layers in a vertical direction [22,23] on the critical properties the model have also been investigated.…”

Section: Introductionmentioning

confidence: 99%

Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study

Žukovič

2021

Preprint

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Critical and in the highly frustrated regime also dynamical properties of the J 1 − J 2 Ising model with competing nearest-neighbor J 1 and second-nearest-neighbor J 2 interactions on a honeycomb lattice are investigated by standard Monte Carlo and parallel tempering simulations. The phase boundary is determined as a function of the coupling ratio for the phase transition between the paramagnetic and ferromagnetic states within R ≡2 the transition remains second-order and complies with the standard Ising universality class. In the highly frustrated regime of R < −0.2 and low temperatures the system tends to freeze to metastable domain states, separated by large energy barriers, which show extremely sluggish dynamics. The resulting huge equilibration and autocorrelation times hinder the analysis of critical properties by using standard Monte Carlo techniques. The parallel tempering approach facilitates much better tunneling through the energy barriers, nevertheless, the convergence to the equilibrium remains beyond the reach even for relatively small system sizes and thus the character of the transition in this region remains to be determined.

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Phase diagram of the frustrated J ₁ − J ₂ transverse field Ising model on the square lattice

Cited by 4 publications

References 18 publications

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

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

Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study

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