Pair supersolid of the extended Bose-Hubbard model with atom-pair hopping on the triangular Lattice

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first order transitions between the Mott Insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/3, 1 and 4/3-filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasi hardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. The transition between the pair supersolid and the pair superfluid is first order, except for the particle-hole symmetric point. We compare the results with those obtained by means of mean-field analysis.Comment: 6 pages, 7 figure

Shape dependent finite-size effect of critical two-dimensional Ising model on a triangular lattice

Using the bond-propagation algorithm, we study the finite-size behavior of the critical two-dimensional Ising model on a finite triangular lattice with free boundaries in five shapes: triangle, rhombus, trapezoid, hexagon and rectangle. The critical free energy, internal energy and specific heat are calculated. The accuracy of the free energy reaches $10^{-26}$. Based on accurate data on several finite systems with linear size up to N=2000, we extract the bulk, surface and corner parts of the free energy, internal energy and specific heat accurately. We confirm the conformal field theory prediction of the corner free energy to be universal and find logarithmic corrections in higher order terms in the critical free energy for the rhombus, trapezoid, and hexagon shaped systems, which are absent for the triangle and rectangle shaped systems. The logarithmic edge corrections due to edges parallel or perpendicular to the bond directions in the internal energy are found to be identical, while the logarithmic edge corrections due to corresponding edges in the free energy and the specific heat are different. The corner internal energy and corner specific heat for angles $\pi/3$, $\pi/2$ and $2\pi/3$ are obtained, as well as higher order corrections. Comparing with the corner internal energy and corner specific heat previously found on a rectangle of the square lattice (Phys. Rev. E. 86 041149 (2012)), we conclude that the corner internal energy and corner specific heat for the rectangle shape are not universal.Comment: arXiv admin note: text overlap with arXiv:1207.454

Crossover phenomena involving the dense O(nn) phase

We explore the properties of the low-temperature phase of the O($n$) loop model in two dimensions by means of transfer-matrix calculations and finite-size scaling. We determine the stability of this phase with respect to several kinds of perturbations, including cubic anisotropy, attraction between loop segments, double bonds and crossing bonds. In line with Coulomb gas predictions, cubic anisotropy and crossing bonds are found to be relevant and introduce crossover to different types of behavior. Whereas perturbations in the form of loop-loop attractions and double bonds are irrelevant, sufficiently strong perturbations of these types induce a phase transition of the Ising type, at least in the cases investigated. This Ising transition leaves the underlying universal low-temperature O($n$) behavior unaffected.Comment: 12 pages, 8 figure

Engineering Surface Critical Behavior of (2+1)-Dimensional O(3) Quantum Critical Points

Surface critical behavior (SCB) refers to the singularities of physical quantities on the surface at the bulk phase transition. It is closely related to and even richer than the bulk critical behavior. In this work, we show that three types of SCB universality are realized in the dimerized Heisenberg models at the (2+1)-dimensional O(3) quantum critical points by engineering the surface configurations. The ordinary transition happens if the surface is gapped in the bulk disordered phase, while the gapless surface state generally leads to the multicritical special transition, even though the latter is precluded in classical phase transitions because the surface is in the lower critical dimension. An extraordinary transition is induced by the ferrimagnetic order on the surface of the staggered Heisenberg model, in which the surface critical exponents violate the results of the scaling theory and thus seriously challenge our current understanding of extraordinary transitions.Comment: v2: slightly revised, published versio

Quantum criticality with two length scales

The theory of deconfined quantum critical points describes phase transitions at temperature T = 0 outside the standard paradigm, predicting continuous transformations between certain ordered states where conventional theory requires discontinuities. Numerous computer simulations have offered no proof of such transitions, however, instead finding deviations from expected scaling relations that were neither predicted by the DQC theory nor conform to standard scenarios. Here we show that this enigma can be resolved by introducing a critical scaling form with two divergent length scales. Simulations of a quantum magnet with antiferromagnetic and dimerized ground states confirm the form, proving a continuous transition with deconfined excitations and also explaining anomalous scaling at T > 0. Our findings revise prevailing paradigms for quantum criticality, with potentially far-reaching implications for many strongly-correlated materials.Comment: 13 pages + supplementary material, very minor changes in v

Typicality at quantum-critical points

We discuss the concept of typicality of quantum states at quantum-critical points, using projector Monte Carlo simulations of an S = 1/2 bilayer Heisenberg antiferromagnet as an illustration. With the projection (imaginary) time τ scaled as τ = aLz , L being the system length and z the dynamic critical exponent (which takes the value z = 1 in the bilayer model studied here), a critical point can be identified which asymptotically flows to the correct location and universality class with increasing L, independently of the prefactor a and the initial state. Varying the proportionality factor a and the initial state only changes the cross-over behavior into the asymptotic large-L behavior. In some cases, choosing an optimal factor a may also lead to the vanishing of the leading finite-size corrections. The observation of typicality can be used to speed up simulations of quantum criticality, not only within the Monte Carlo approach but also with other numerical methods where imaginary-time evolution is employed, e.g., tensor network states, as it is not necessary to evolve fully to the ground state but only for sufficiently long times to reach the typicality regime.Project supported by the National Natural Science Foundation of China (Grant Nos. 11734002 and 11775021), the National Science Foundation (Grant No. DMR-1710170), and a Simons Investigator Award. (11734002 - National Natural Science Foundation of China; 11775021 - National Natural Science Foundation of China; DMR-1710170 - National Science Foundation; Simons Investigator Award)Accepted manuscrip

Exact finite-size corrections and corner free energies for the c = - 2 universality class

We consider the partition functions of the anisotropic dimer model on the rectangular (2. M - 1) × (2. N - 1) lattice with (a) free and (b) cylindrical boundary conditions with a single monomer residing on the boundary. We express (a) and (b) in terms of a principal partition function with twisted boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the free energy for both cases (a) and (b). We confirm the conformal field theory prediction for the corner free energy of these models, and find the central charge is c = - 2. We also show that the dimer model on the cylinder with an odd number of sites on the perimeter exhibits the same finite-size corrections as on the plane.</p