Condensed Matter

This seminar will focus on two cases where the interplay of topology and interactions allows for phases that go beyond simple quasi-particle descriptions. Both models are amenable to sign free auxiliary field quantum Monte Carlo simulations.

First, we design a two-dimensional model consisting of four Dirac-fermion layers on the square lattice. The interaction is given by a four-fermion term where each fermion is from a different layer. In the uncorrelated case, the topology is determined by a Z-valued winding number and previous studies, often using the bulk-boundary correspondence and dimensional reduction arguments, predict the reduction to a Z4 classification in the presence of correlations. An adiabatic path between formerly distinct phases has to visit a strongly interacting state that cannot be described on a mean-field level. We study the phase diagram of the full bulk system and find a symmetry broken state separating topological distinct phases. An attempt to frustrate the ordered state introduces a first order phase transition [Fig. 1 (left)].

Second, we consider Dirac electrons on the honeycomb lattice Kondo coupled to spin-1/2 degrees of freedom on the kagome lattice. The interactions between the spins are chosen along the lines of the Balents-Fisher-Girvin model that is known to host a Z2 spin liquid and a fer- romagnetic phase. While in the ferromagnetic phase the Dirac electrons acquire a gap, they remain massless in the Z2 spin liquid phase due to the breakdown of Kondo screening. Since our model has an odd number of spins per unit cell, this phase is a non-Fermi liquid, also called fractionalized Fermi liquid, that violates the conventional Luttinger theorem, which relates the Fermi volume to the particle density in a Fermi liquid. We probe the Kondo breakdown in this non-Fermi liquid phase via conventional observables such as the spectral function, and also by studying the mutual information between the electrons and the spins [Fig. 1 (right)].

Figure 1: Schematic sketch of the phase diagram discussed during the beginning of the seminar (left). Numerical Results consistent with a FL* to magnetic insulator transition as subject of the second half (right).

In our previous work (Phys. Rev. Lett. 121, 046401 (2018)), we found a quantum spin liquid phase with spinon Fermi surface in the two dimensional spin-1/2 Heisenberg model with four-spin ring exchange on a triangular lattice. In this work we dope the spinon Fermi surface phase by studying the t-J model with four-spin ring exchange. We perform density matrix renormalization group calculations on four-leg cylinders of a triangular lattice and find that the dominant pair correlation function is that of a pair density wave, i.e. it is oscillatory while decaying with distance with a power law. The doping dependence of the period is studied. This is the first example where pair density wave is the dominant pairing in a generic strongly interacting system where the pair density wave cannot be explained as a composite order and no special symmetry is required. Reference: 1. arXiv:1803.00999 [cond-mat.str-el] (Phys. Rev. Lett. 121, 046401 (2018)) 2. arXiv:1811.06538 [cond-mat.str-el]

A single layer graphene hides many body effects in the dense viscous 
fluid of p-pi electrons, Bilayer graphene, with AA and AB registry, on 
the other hand, exposes some of them. A twisted bilayer springs more 
surprises. We discuss recently seen superconductivity in twisted bilayer 
graphene. Resonating valence bond (RVB) physics contained in the dense 
electron fluid in graphene is invoked [1]. RVB fails to produce 
superconductivity in neutral graphene, as carrier are absent at the 
Fermi level. In a twisted bilayer, interlayer tunneling adds equal 
number of electron and hole carriers in Moire superlattice of dominant 
AA registry. These carriers use RVB pairing and develop charge -2e and 
+2e Cooper pair correlations, in spite of Coulomb repulsions. Resulting 
Moire lattice of Cooper pair puddles form a Josephson lattice. Coulomb 
blockade makes it a Bosonic Mott insulator. Gate voltage dopes the Bose 
Mott insulator and interesting consequences follow.

[1] G. Baskaran, arXiv:1804.00627

Systems of strongly interacting particles can give rise to topological phases beyond non-interacting limit.  Although unique features of strongly interacting topological phases, such as fractionalization of quantum degrees of freedom, have important applications in quantum information processing, these topological phases are still far from experimental realizations. In this talk, by presenting constructions of two strongly interacting topological phases, I will argue the key mechanism of their realizations is to add interactions near topological phase transitions.  I will first introduce a model of interacting Majorana fermions that describes a superconducting phase with Fibonacci topological order. Then I will show that a correlated fluid of electrons and holes, dubbed fractional excitonic insulator phase, can exhibit a fractional quantum Hall effect at zero magnetic field. I will present physical evidence and conjecture that this phase can be realized in a higher angular momentum excitonic paired system in the presence of interactions.   

Finding a quantum phase transition between two even well-studied phases of matter can be a hard problem. Free probability theory suggests a new method which can give an answer if the Hamiltonians of two phases satisfy certain conditions. In the latter case, the spectral gap behavior can be calculated without solving the full Hamiltonian but using probabilistic estimation instead. As an example, I will consider generic artificial topological systems created by a periodic drive, including Floquet Majorana modes, and show how FPT can be used to predict and characterize disorder-driven phase transitions.

See also: Phys. Rev. Lett. 121, 126803