The discovery of high temperature superconductivity inspired a number of novel proposals, one of which, put forward by C.M.Varma, involves the breaking of time-reversal symmetry to explain the physics of the underdoped pseudogap phase. It was proposed that time-reversal symmetry is spontaneously broken as a result of strong repulsion between the Cu-O electrons to form loop-currents in the system. In this work, we developed a general theory to study the quantum phase transitions in the 2 dimensional strongly interacting electronic systems in which time-reversal symmetry is spontaneously broken in the ground state. We first applied the theory of magnetic groups to identify electronic current-loop patterns in two physically relevant systems: (i) 2-band model involving spinless electrons on a honeycomb lattice with next-nearest-neighbor interactions; (ii) 3-band
CuO2 model with and without lattice distortions. Next, by examining the correlation function within the standard ring and ladder Dyson series approximations, we identify the effective Hamiltonian with the relevant interactions responsible for creating low-energy fluctuations near the quantum critical point. The mean-field analysis of this effective Hamiltonian elucidated the fact that time-reversal symmetry breaking in a 2-band model is in the same universality class as the interband particle-hole pair condensation instability which occurs in the semi-conductors under large enough particle-hole attraction. Using Hubbard-Stratonovich transformation and functional integral method, we are able to investigate this instability and the static susceptibility in the condensed phase both in half-filling and doped case. Away from half-filling, because the condensates are metallic and couple to the gapless collective intraband particle-hole excitations, we find that the static susceptibility is generically negative as a result of this coupling, which implies that the condensates are unstable.
As a minimal fermionic model with kinetic frustration, we study a system of spinless fermions in the lowest band of a triangular lattice with nearest-neighbor repulsion. We find that the combination of interactions and kinetic frustration leads to spontaneous symmetry breaking in various ways. Time-reversal symmetry can be broken by two types of loop current patterns, a chiral one and one that breaks the translational lattice symmetry. Moreover, the translational symmetry can also be broken by a density wave forming a kagome pattern or by a Peierls-type trimerization characterized by enhanced correlations among the sites of certain triangular plaquettes (giving a plaquette-centered density wave). We map out the phase diagram as it results from leading-order Ginzburg-Landau mean-field theory. Several experimental realizations of the type of system under study are possible with ultracold atoms in optical lattices.
The emergence of superconductivity in doped Mott insulators has been debated for decades. In this paper, we report the theoretical discovery of a time-reversal symmetry breaking superconducting ground state in the doped Mott insulator (described by the well known
t-
J model) on honeycomb lattice, based on a recently developed variational method: the Grassmann tensor product state approach. As a benchmark, we use exact diagonalization and density-matrix renormalization methods to check our results on small clusters. We find systematic consistency for the ground-state energy as well as other physical quantities, such as the staggered magnetization. At low doping, the superconductivity coexists with antiferromagnetic ordering.
We investigate the properties of the nearest-neighbor singlet pairing and the emergence of
d-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott-insulating state, we confirm the emergence of
d-wave superconductivity, in agreement with earlier works. We show that a small but finite
J2 spin coupling between next-nearest neighbors stabilizes
d-wave symmetry compared to the extended
s-wave scenario. At small hole doping, to minimize the energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a
d+id singlet pairing assigned to one valley and a $d\ensuremath{-}id$ singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral
d+id symmetry and breaking time-reversal symmetry. Then, we apply the functional renormalization group and study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half filling. We discuss possible applications to strongly correlated compounds with copper hexagonal planes such as In
3Cu
2VO
9. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.
An effective model in the isolated dimer limit of the Kitaev-type model on a decorated honeycomb lattice is investigated at finite temperature. The ground state of this model is exactly shown to be a chiral spin liquid with spontaneous breaking of time reversal symmetry. We elab- orate the finite-temperature phase diagram by using the mean-field approximation and Monte Carlo simulation. We find that the phase transition between the high-temperature paramagnetic phase and the low-temperature chiral spin liquid phase is always of second order in the Monte Carlo results, although a tricritical point appears in the mean-field phase diagram. The finite-size scaling analysis of the Monte Carlo data suggests that the phase transition belongs to the two-dimensional Ising universality class.
Topological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous systems? Here we construct a soluble chiral amorphous quantum spin liquid by extending the Kitaev honeycomb model to random lattices with fixed coordination number three. The model retains its exact solubility but the presence of plaquettes with an odd number of sides leads to a spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram displaying Abelian as well as a non-Abelian quantum spin liquid phases with a remarkably simple ground state flux pattern. Furthermore, we show that the system undergoes a finite-temperature phase transition to a conducting thermal metal state and discuss possible experimental realisations.