Recently, generative machine-learning models have gained popularity in physics, driven by the goal of improving the efficiency of Markov chain Monte Carlo techniques and of exploring their potential in capturing experimental data distributions. Motiv
ated by their ability to generate images that look realistic to the human eye, we here study generative adversarial networks (GANs) as tools to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters, such as temperature. We propose ways to efficiently represent the physical states, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. We present a detailed evaluation of the various modifications, using the two-dimensional XY model as an example, and find considerable improvements in our proposed implicit generative model. It is also shown that the model can reliably generate samples in the vicinity of the phase transition, even when it has not been trained in the critical region. On top of using the samples generated by the model to capture the phase transition via evaluation of observables, we show how the model itself can be employed as an unsupervised indicator of transitions, by constructing measures of the models susceptibility to changes in tuning parameters.
We consider 2+1 dimensional conformal gauge theories coupled to additional degrees of freedom which induce a spatially local but long-range in time $1/(tau-tau)^2$ interaction between gauge-neutral local operators. Such theories have been argued to d
escribe the hole-doped cuprates near optimal doping. We focus on a SU(2) gauge theory with $N_h$ flavors of adjoint Higgs fields undergoing a quantum transition between Higgs and confining phases: the $1/(tau-tau)^2$ interaction arises from a spectator large Fermi surface of electrons. The large $N_h$ expansion leads to an effective action containing fields which are bilocal in time but local in space. We find a strongly-coupled fixed point at order $1/N_h$, with dynamic critical exponent $z > 1$. We show that the entropy preserves hyperscaling, but nevertheless leads to a linear in temperature specific heat with a co-efficient which has a finite enhancement near the quantum critical point.
The study of topological bandstructures is an active area of research in condensed matter physics and beyond. Here, we combine recent progress in this field with developments in machine-learning, another rising topic of interest. Specifically, we int
roduce an unsupervised machine-learning approach that searches for and retrieves paths of adiabatic deformations between Hamiltonians, thereby clustering them according to their topological properties. The algorithm is general as it does not rely on a specific parameterization of the Hamiltonian and is readily applicable to any symmetry class. We demonstrate the approach using several different models in both one and two spatial dimensions and for different symmetry classes with and without crystalline symmetries. Accordingly, it is also shown how trivial and topological phases can be diagnosed upon comparing with a generally designated set of trivial atomic insulators.
The Mott insulating phase of the parent compounds is frequently taken as starting point for the underdoped high-$T_c$ cuprate superconductors. In particular, the pseudogap state is often considered as deriving from the Mott insulator. In this work, w
e systematically investigate different weakly-doped Mott insulators on the square and triangular lattice to clarify the relationship between the pseudogap and Mottness. We show that doping a two-dimensional Mott insulator does not necessarily lead to a pseudogap phase. Despite its inherent strong-coupling nature, we find that the existence or absence of a pseudogap depends sensitively on non-interacting band parameters and identify the crucial role played by the van Hove singularities of the system. Motivated by a SU(2) gauge theory for the pseudogap state, we propose and verify numerically a simple equation that governs the evolution of characteristic features in the electronic scattering rate.
We present a systematic classification and analysis of possible pairing instabilities in graphene-based moire superlattices. Motivated by recent experiments on twisted double-bilayer graphene showing signs of triplet superconductivity, we analyze bot
h singlet and triplet pairing separately, and describe how these two channels behave close to the limit where the system is invariant under separate spin rotations in the two valleys, realizing an SU(2)$_+$ $times$ SU(2)$_-$ symmetry. Further, we discuss the conditions under which singlet and triplet can mix via two nearly degenerate transitions, and how the different pairing states behave when an external magnetic field is applied. The consequences of the additional microscopic or emergent approximate symmetries relevant for superconductivity in twisted bilayer graphene and ABC trilayer graphene on hexagonal boron nitride are described in detail. We also analyze which of the pairing states can arise in mean-field theory and study the impact of corrections coming from ferromagnetic fluctuations. For instance, we show that, close to the parameters of mean-field theory, a nematic mixed singlet-triplet state emerges. Our study illustrates that graphene superlattices provide a rich platform for exotic superconducting states, and allow for the admixture of singlet and triplet pairing even in the absence of spin-orbit coupling.
We describe square lattice spin liquids which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have non-zero scalar spin
chirality, which implies the appearance of spontaneous orbital charge currents in the bulk (even in the insulator); but in some cases, orbital currents are non-zero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with $mathbb{Z}_2$ and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the Neel state.
An ordered state in the spin sector that breaks parity without breaking time-reversal symmetry, i.e., that can be considered as dynamically generated spin-orbit coupling, was proposed to explain puzzling observations in a range of different systems.
Here we derive severe restrictions for such a state that follow from a Ward identity related to spin conservation. It is shown that $l=1$ spin-Pomeranchuk instabilities are not possible in non-relativistic systems since the response of spin-current fluctuations is entirely incoherent and non-singular. This rules out relativistic spin-orbit coupling as an emergent low-energy phenomenon. We illustrate the exotic physical properties of the remaining higher angular momentum analogues of spin-orbit coupling and derive a geometric constraint for spin-orbit vectors in lattice systems.
We analyze the possible interaction-induced superconducting instabilities in noncentrosymmetric systems based on symmetries of the normal state. It is proven that pure electron-phonon coupling will always lead to a fully gapped superconductor that do
es not break time-reversal symmetry and is topologically trivial. We show that topologically nontrivial behavior can be induced by magnetic doping without gapping out the resulting Kramers pair of Majorana edge modes. In case of superconductivity arising from the particle-hole fluctuations associated with a competing instability, the properties of the condensate crucially depend on the time-reversal behavior of the order parameter of the competing instability. When the order parameter preserves time-reversal symmetry, we obtain exactly the same properties as in case of phonons. If it is odd under time-reversal, the Cooper channel of the interaction will be fully repulsive leading to sign changes of the gap and making spontaneous time-reversal symmetry breaking possible. To discuss topological properties, we focus on fully gapped time-reversal symmetric superconductors and derive constraints on possible pairing states that yield necessary conditions for the emergence of topologically nontrivial superconductivity. These conditions might serve as a tool in the search for topological superconductors. We also discuss implications for oxides heterostructures and single-layer FeSe.
Thin sheets deposited on a substrate and interfaces of correlated materials offer a plethora of routes towards the realization of exotic phases of matter. In these systems, inversion symmetry is broken which strongly affects the properties of possibl
e instabilities -- in particular in the superconducting channel. By combining symmetry and energetic arguments, we derive general and experimentally accessible selection rules for Cooper instabilities in noncentrosymmetric systems which yield necessary and sufficient conditions for spontaneous time-reversal-symmetry breaking at the superconducting transition and constrain the orientation of the triplet vector. We discuss in detail the implications for various different materials. For instance, we conclude that the pairing state in thin layers of Sr$_2$RuO$_4$ must, as opposed to its bulk superconducting state, preserve time-reversal symmetry with its triplet vector being parallel to the plane of the system. All pairing states of this system allowed by the selection rules are predicted to display topological Majorana modes at dislocations or at the edge of the system. Applying our results to the LaAlO$_3$/SrTiO$_3$ heterostructures, we find that while the condensates of the (001) and (110) oriented interfaces must be time-reversal symmetric, spontaneous time-reversal-symmetry breaking can only occur for the less studied (111) interface. We also discuss the consequences for thin layers of URu$_2$Si$_2$ and UPt$_3$ as well as for single-layer FeSe. On a more general level, our considerations might serve as a design principle in the search for time-reversal-symmetry-breaking superconductivity in the absence of external magnetic fields.
