Phase diagram of the quantum Ising model on a triangular lattice under external field

Liao, Yuan Da; Li, Han; Yan, Zheng; Wei, Haotian; Li, Wei; Qi, Yang; Meng, Zi Yang

doi:10.1103/physrevb.103.104416

Cited by 24 publications

(13 citation statements)

References 36 publications

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“…As shown in Fig. 1(b), the phase diagram of the model with transverse field (to introduce quantum fluctuations) has been mapped out from previous theoretical and numerical works [19][20][21][22]. The constrained problem we would like to solve is seeking the ground state at the limits where h and T are approaching zero.…”

Section: Microscopic Spin Modelmentioning

confidence: 99%

“…The quantum annealing is implemented by utilizing the quantum Monte Carlo (QMC) simulation [29][30][31], and we adopt a continuous-time QMC -stochastic series expansion (SSE) method [32][33][34] to avoid the Trotter discretization error [29,35]. The QMC schemes have been successfully employed in many previous works (including ours) on quantum Ising models [21,22,36].…”

Section: Microscopic Spin Modelmentioning

confidence: 99%

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Sweeping quantum annealing algorithm for constrained optimization problems

Yan¹,

Zhou²,

Wang³

et al. 2021

Preprint

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As a typical quantum computing algorithm, quantum annealing is widely used in the optimization of glass-like problems to find the best solution. However, the optimization problems in constrained complex systems usually involve topological structures, and the performance of the quantum annealing algorithm is still largely unknown. Here, we take an Ising system as a typical example with local constraints accompanied by intrinsic topological properties that can be implemented on quantum computing platforms such as the D-wave machine, and study the effectiveness of the quantum annealing algorithm in its optimization and compare it with that of the thermal annealing. We find that although conventional quantum annealing is difficult for the optimization of constrained topological problems, a generalized algorithm --- the sweeping quantum annealing method --- can be designed and solve the problem with better efficiency than both conventional quantum and thermal annealing algorithms. The sweeping quantum annealing algorithm, therefore, opens up a promising avenue for quantum computing of constrained problems and can be readily employed on the optimizations in quantum material design, engineering, and even social sciences.

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Section: Microscopic Spin Modelmentioning

confidence: 99%

Section: Microscopic Spin Modelmentioning

confidence: 99%

Sweeping quantum annealing algorithm for constrained optimization problems

Yan¹,

Zhou²,

Wang³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The effective theory given in Eq. 12 is in the same universality class of the six-state clock model [32][33][34][35][36], and it enables us to have some guesses for finite temperature phases. For d = 2 (d is the spatial dimension) case, if the system doesn't have particle-hole symmetry, then the total dimension D is still 2 (D is the quantum dimension).…”

mentioning

confidence: 98%

Mott Insulator-Density Ordered Superfluid Transition and "Shamrock Transition" in a Frustrated Triangle Lattice

Chen¹

2021

Preprint

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Density order is usually a consequence of the competition between long-range and short-range interactions. Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions. This transition is found in a Bose-Hubbard model on a frustrated triangle lattice with an extra pairing term. Further, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau-Ginzburg paradigm. Across this transition, a U(1) symmetry is emergent, while the symmetry in each density ordered superfluid is Z2 × Z3. Because there emerges a shamrock-like degenerate ground state in parameter space, we call the transition "shamrock transition". Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.

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“…Introduction.-In quantum many-body systems, topologically ordered phases [1][2][3][4] and their fractionalized excitations [2,5] have attracted much attention because they hold the promise of providing solutions to many mysteries of highly entangled quantum matter such as unconventional superconductors [6][7][8], quantum moiré materials [9,10], frustrated quantum magnets [11][12][13][14][15][16][17][18], andmore recently-programmable Rydberg quantum simulators [19][20][21][22][23]. Concomitantly, the quantum phase transitions between topologically ordered phases and conventional symmetry-breaking states have also been actively investigated with a variety of theoretical and numerical approaches [22][23][24][25][26][27][28][29][30][31][32].…”

mentioning

confidence: 99%

Fully packed quantum loop model on the triangular lattice: Hidden vison plaquette phase and cubic phase transitions

Zheng¹,

Ran²,

Wang³

et al. 2022

Preprint

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Quantum loop and dimer models are prototypical correlated systems with local constraints, whose generic solutions for different lattice geometries and parameter regimes are still missing due to the lack of controlled methods to solve such systems in the thermodynamic limit. Here, we obtain, via the newly developed sweeping cluster quantum Monte Carlo algorithm, the phase diagram of the triangular-lattice fully packed quantum loop model (quantum dimer model with two dimers per site). We find that as the interaction turns from attractive to repulsive, the system has a first-order transition from a lattice nematic (LN) solid to a novel vison plaquette (VP) solid without dimer density modulations but with off-diagonal order. Further increasing the dimer repulsion towards the Rokhsar-Kivelson point, the VP phase experiences a continuous transition to an even Z2 quantum spin liquid (QSL) phase. Our results reveal the LN-to-VP first-order transition is triggered by the intricate change from face-to corner-cubic anisotropy of the O(3) vison order parameter, and the VP-to-QSL continuous transition is of the cubic universality class, which is very close to the (2+1)D O(3) one, in full consistency with the recent conformal bootstrap findings on the cubic fixed point.

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Phase diagram of the quantum Ising model on a triangular lattice under external field

Cited by 24 publications

References 36 publications

Sweeping quantum annealing algorithm for constrained optimization problems

Sweeping quantum annealing algorithm for constrained optimization problems

Mott Insulator-Density Ordered Superfluid Transition and "Shamrock Transition" in a Frustrated Triangle Lattice

Fully packed quantum loop model on the triangular lattice: Hidden vison plaquette phase and cubic phase transitions

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