Hard-core bosons on a triangular lattice with nearest neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.

We determine the quantum phase diagram of the antiferromagnetic spin-1/2 XXZ model on the triangular lattice as a function of magnetic field and anisotropic coupling Jz. Using the density matrix renormalization group (DMRG) algorithm in two dimensions we establish the locations of the phase boundaries between a plateau phase with 1/3 Néel order and two distinct coplanar phases. The two coplanar phases are characterized by a simultaneous breaking of both translational and U(1) symmetries, which is reminiscent of supersolidity. A translationally invariant umbrella phase is entered via a first order phase transition at relatively small values of Jz compared to the corresponding case of ferromagnetic hopping and the classical model. The phase transition lines meet at two tricritical points on the tip of the lobe of the plateau state, so that the two coplanar states are completely disconnected. Interestingly, the phase transition between the plateau state and the upper coplanar state changes from second order to first order for large values of Jz > ∼ 2.5J.PACS numbers: 75.10. Jm, 67.80.kb, 05.30.Jp Competing interactions between quantum spins can prevent conventional magnetic order at low temperatures. In the search of interesting and exotic quantum phases frustrated systems are therefore at the center of theoretical and experimental research in different areas of physics . One of the most straight-forward frustrated system is the spin-1/2 antiferromagnet (AF) on the triangular lattice, which was also the first model to be discussed as a potential candidate for spin-liquid behavior without conventional order by Anderson [2]. It is now known that the isotropic Heisenberg model on the triangular lattice is not a spin liquid and does show order at zero temperature [3]. Nonetheless, the phase diagram as a function of magnetic field is still actively discussed with recent theoretical calculations [4,5] as well as experimental results [6-9] on Ba 3 CoSb 2 O 9 , which appears to be very well described by a triangular AF. Interesting phases have also been found for anisotropic triangular lattices [11][12][13] and for the triangular extended Hubbard model [14]. Hard-core bosons with nearest neighbor interaction on a triangular lattice correspond to the xxz model with ferromagnetic exchange in the xy-plane, which has been studied extensively [15][16][17][18][19][20]. In this case a so-called supersolid phase near half-filling has been established for large interactions [15], which is characterized by two order parameters, namely a superfluid density and a √ 3 × √ 3 charge density order. Impurity effects show that the two order parameters are competing [17] and the transition to the superfluid state is first order [19,20].However, surprisingly little attention has been paid to the role of an antiferromagnetic anisotropic exchange interaction away from half-filling [24][25][26][27], even though the XXZ model on the triangular lattice H = J ij (Ŝ x iŜ x j +Ŝ y iŜ y j ) + J z ij Ŝ z iŜ z j − B iŜ z i , (1) is arguable one of the...

We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atom-atom interaction and atom-light coupling induces a rich phase diagram. A novel superradiant solid (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance transition, here both the solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by large scale quantum Monte Carlo simulations.

We use large scale quantum Monte Carlo simulations to study an extended Hubbard model of hard core bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at 1/3 filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. We present a theory in terms of an easy plane noncompact CP^{1} gauge theory describing the phase transition at 1/3 filling. Utilizing large scale quantum Monte Carlo simulations with parallel tempering in the canonical ensemble up to 15552 spins, we provide evidence that the phase transition is continuous at exactly 1/3 filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality.

We study the extended Hubbard model on the triangular lattice as a function of filling and interaction strength. The complex interplay of kinetic frustration and strong interactions on the triangular lattice leads to exotic phases where long-range charge order, antiferromagnetic order, and metallic conductivity can coexist. Variational Monte Carlo simulations show that three kinds of ordered metallic states are stable as a function of nearest neighbor interaction and filling. The coexistence of conductivity and order is explained by a separation into two functional classes of particles: part of them contributes to the stable order, while the other part forms a partially filled band on the remaining substructure. The relation to charge ordering in charge transfer salts is discussed.

We study the properties of the Bose-Hubbard model for square and cubic superlattices. To this end we generalize a recently established effective potential Landau theory for a single component to the case of multi components and find not only the characteristic incompressible solid phases with fractional filling, but also obtain the underlying quantum phase diagram in the whole parameter region at zero temperature. Comparing our analytic results with corresponding ones from quantum Monte Carlo simulations demonstrates the high accuracy of the generalized effective potential Landau theory (GEPLT). Finally, we comment on the advantages and disadvantages of the GEPLT in view of a direct comparison with a corresponding decoupled mean-field theory.

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Machine learning algorithms provide a new perspective on the study of physical phenomena. In this paper, we explore the nature of quantum phase transitions using multi-color convolutional neural-network (CNN) in combination with quantum Monte Carlo simulations. We propose a method that compresses (d + 1)-dimensional space-time configurations to a manageable size and then use them as the input for a CNN. We benchmark our approach on two models and show that both continuous and discontinuous quantum phase transitions can be well detected and characterized. Moreover we show that intermediate phases, which were not trained, can also be identified using our approach.Machine learning, especially deep learning, has recently shown to be a very powerful tool in the fields of image classification, speech recognition, video activity recognition, machine translation, game playing and so on 1-3 . The basic idea is to train a machine with large datasets such that it can thereafter process and characterize new data. A typical example is image recognition, where a large number of images are used as the training set. During the training process, a non-linear variational function with images as input and for example the names of objects as output is optimized with respect to a cost function. Using this optimized function, the machine can then recognize the objects in other testing images by knowing their key features.An important task in condensed matter physics is to characterize different phases of matter and transitions between them 4,5 . Phases can for example be characterized by local order parameters in Landau's theory of spontaneously symmetry breaking 6 , by topological invariants in topological phases 7 , or by their dynamical properties as in the many-body localized phase 8 . The main difficulty of this approach is to find characteristic and universal properties of a given phase before we can identify it in a given physical system. In contrast, machine learning techniques promise to classify the phases automatically given a sufficiently large training set is provided. The deep learning algorithm, which we use in this work, is a method that is capable to learn the key features of individual phases and to classify them directly from "raw data" (e.g., the partition function or the ground state wave function). Machine learning is a powerful tool compared to conventional approaches and already inspired physicists to come up with new methods to recognize phases in various settings [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] .A natural way to use machine learning to identify different phases of matter is with the aid of Monte Carlo method 28 . By stochastically moving through configuration space according to a partition function, a large number of samples can be obtained and labelled by different phases. These can then be fed into deep learning algorithms as training sets to classify phases and also detect phase transitions 9-17 . Considering each sample as a snap-shot photo, the classical phase ...