Quantum Matter

It is well-known that sufficiently strong interactions can destabilize some SPT phases of free fermions, while others remain stable even in the presence of interactions. It is also known that certain interacting phases cannot be realized by free fermions. In this talk, we will study both of these phenomena in low dimensions and determine the map from free to interacting SPT phases for an arbitrary unitary symmetry. We will also describe how to compute invariants characterizing interacting phases for free band Hamiltonians with symmetry (in any dimension) using only representation theory.

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body ``scar states'' in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at infinite temperature that can be represented exactly as matrix product states with finite bond dimension, for both periodic boundary conditions (two exact E = 0 states) and open boundary conditions (two E = 0 states and one each E =± √2). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in 1D at infinite temperature. We show that the nearby many-body scar states with energies E ~± 1.33 andE ~ ± 2.66 can be well approximated as ``quasiparticle excitations" on top of our exact E = 0 states, and propose a quasiparticle explanation of the strong oscillations observed in experiments.

Experiments on organic crystals whose structure is well-described by the two-dimensional triangular lattice have found a lack of magnetic ordering down to the lowest accessible temperatures, indicative of a quantum spin liquid phase; however, the precise nature of this phase remains an open question.  In this talk, I present strong evidence that the triangular lattice Hubbard model at half filling, a physically motivated model of these organic crystals, realizes a chiral spin liquid phase.  In particular, I show that the model has a nonmagnetic insulating phase between a metallic phase for weak interactions and a magnetically ordered phase for strong interactions, and that the intermediate phase exhibits the expected properties of a chiral spin liquid: spontaneous breaking of time-reversal symmetry, topological ground state degeneracy, a quantized spin Hall effect, and characteristic level counting in the entanglement spectrum.  These results were obtained using the infinite-system density matrix renormalization group (iDMRG) method in a mixed real- and momentum-space basis; in the talk, I will also discuss the benefits of this mixed-space approach to DMRG in general, including its applicability to systems such as twisted bilayer graphene for which a large unit cell makes real-space DMRG impractical. 

Supersymmetry (SUSY) has not been verified so far as a fundamental symmetry in particle physics. Emergent phenomena in condensed matter physics bring the possibility of realizing SUSY as an IR symmetry. We show that 2+1D N=2 Nf=2 supersymmetric quantum electrodynamics (SQED3) with dynamical gauge bosons and fermionic gauginos emerges naturally at the tricritical point of nematic pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator hosting three Dirac cones, such as the topological Kondo insulator SmB6. It provides a first example of emergent supersymmetric gauge theory in condensed matter systems. We also investigate the possibility of emergent 3+1D SUSY theory in lattice models. By constructing an explicit fermionic lattice model featuring two 3D Weyl nodes, we find a continuous PDW quantum phase transition as a function of attractive Hubbard interaction. We further show that N=1 3+1D SUSY emerges at the PDW transition, which we believe is the first realization of emergent 3+1D space-time SUSY in microscopic lattice models. Supersymmetry allows us to determine certain critical exponents and the optical conductivity at the strongly coupled fixed point exactly, which may be measured in future experiments.

Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as square of the commutator (out-of-time-ordered correlator), operator entanglement entropy etc. In this talk, we discuss operator dynamics in three representative models: a 2-local spin model with all-to-all interaction, a chaotic spin chain with long-range interactions,  and the quantum linear map. In the first two examples, we explore the operator dynamics by using the quantum Brownian circuit approach and transform the operator spreading into a classical stochastic problem. Although the speeds of scrambling are quite different, a simple operator can eventually approach a "highly entangled" operator with operator entanglement entropy taking a volume law value (close to the Page value). Meanwhile, the spectrum of the operator reduced density matrix develops a universal spectral correlation which can be characterized by the Wishart random matrix ensemble.  In contrast, in the third example (the quantum linear map), although the square of commutator can increase exponentially with time, a simple operator does not scramble but performs chaotic motion in the operator basis space determined by the classical linear map. We show that once we modify the quantum linear map such that operator can mix in the operator basis, the operator entanglement entropy can grow and eventually saturate to its Page value, thus making it a truly quantum chaotic model.

This year there appear several amazing experiments  in the graphene moire superlattices.  In this talk I will focus on the ABC trilayer graphene/h-BN system. Mott-like  insulators at 1/4 and 1/2 of the valence band have already been reported by Feng Wang’s group at Berkeley. The sample is dual gated on top and bottom with voltage V_t and V_b.  V_t+V_b controls the density of electrons. Interestingly we find that the displacement field D=V_t-V_b can control both the topology and the bandwidth of the valence band. For one sign of D (for example D>0), there are two narrow Chern bands with opposite Chern numbers C=3,-3 for the two valleys. For D<0, the bands of the two valleys are trivial and have localized Wannier orbitals on a triangular lattice.  As a result, the physics is governed by a spin-valley Hubbard model on a triangular lattice. This talk focuses on the D<0 side and  consists of two parts:  (1) I will provide the details of this spin-valley Hubbard model and discuss some subtleties special to the moire systems.   (2) In the second part I want to show some of our theoretical attempts on this Hubbard model. First I will show that this system is a perfect platform for studying metal-insulating transition. I will provide a theory of continuous Mott transition between a Fermi liquid and a spinon Fermi surface Mott insulator. Second I will discuss some possible metallic phases upon doping away from the Mott insulator.  Unlike the familiar spin 1/2 case, the spin-valley Hubbard model may not be in a conventional Fermi liquid phase even in the over-doped region. I will provide some candidates of possible unconventional metals based on a six-flavor slave boson theory for the hole doped side.

References:

Feng Wang et.al. arxiv: 1803.01985

Ya-Hui Zhang, Dan Mao, Yuan Cao, Pablo Jarillo-Herrero and T. Senthil.  arXiv:1805.08232

Ya-Hui Zhang and T. Senthil, arxiv: 1809.05110

Ya-Hui Zhang and T. Senthil, ongoing work

We implement projective quantum Monte Carlo (PQMC) methods to simulate quantum annealing on classical computers. We show that in the regime where the systematic errors are well controlled, PQMC algorithms are capable of simulating the imaginary-time dynamics of the Schroedinger equation both on continuous space models and discrete basis systems. We also demonstrate that the tunneling time of the PQMC method is quadratically faster than the one of incoherent quantum annealing. It shows remarkable stability when applied to frustrated systems compared to finite-temperature path integral Monte Carlo algorithm, the method mostly chosen to do comparisons with quantum annealers. However, a major drawback of the PQMC method comes from the finite number of random walkers needed
to implement the simulations. It grows exponentially with the system size when no or poor guiding wave-functions are utilized. Nevertheless, we demonstrate that when good enough guiding wave-functions are used – in our case we choose artificial neural networks – the computational complexity seems to go from exponential to polynomial in the system size. We advocate for a search of more efficient guiding wave functions since they could determine when PQMC simulations are feasible on classical computers, a question closely related to a provable need or speed-up of a quantum computer.

References:
- E. M. Inack and S. Pilati, Phys. Rev. E 92, 053304 (2015)
- E. M. Inack, G. Giudici, T. Parolini, G. Santoro and S. Pilati, Phys. Rev. A 97, 032307 (2018)
- E. M. Inack, G. Santoro, L. Dell’Anna, and S. Pilati, arXiv:1809.03562v1

Applying a chemical potential bias to a conductor drives the system out of equilibrium into a current carrying non-equilibrium state.  This current flow is associated with entropy production in the leads, but it remains poorly understood under what conditions the system is driven to local equilibrium by this process.  We investigate this problem using two toy models for coherent quantum transport of diffusive fermions:  Anderson models in the conducting phase and a class of random quantum circuits acting on a chain of qubits, which exactly maps to an interacting fermion problem. Under certain conditions, we find that the long-time states in both models exhibit volume-law mutual information and entanglement, in striking violation of local equilibrium.  Extending this analysis to Anderson metal-insulator transitions, we find that the volume-law entanglement scaling persists at the critical point up to mobility edge effects.  This work points towards a broad class of examples of physical systems where volume-law entanglement can be sustained, and potentially harnessed, despite strong coupling of the system to its surrounding environment. 

Despite much theoretical effort, there is no complete theory of the “strange” metal phase of the high temperature 

superconductors, and its linear-in-temperature resistivity. This phase is believed to be a strongly-interacting metallic 

phase of matter without fermionic quasiparticles, and is virtually impossible to model accurately using traditional

perturbative field-theoretic techniques. Recently, progress has been made using large-N techniques based on the 

solvable Sachdev-Ye-Kitaev (SYK) model, which do not involve expanding about any weakly-coupled limit. I will 

describe constructions of solvable models of strange metals based on SYK-like large-N limits, which can reproduce  

some of the experimentally observed features of strange metals and adjoining phases. These models, and further 

extensions, could possibly pave the way to developing a controlled theoretical understanding of the essential building 

blocks of the electronic state in correlated-electron superconductors near optimal doping.

We discuss some algebraic quantum field theory (AQFT) ingredients that should be useful in defining a tensor network describing a Lorentzian space-time.

We look into toy models that approximate Minkowski space and show how Lorentz boosts are approximately recovered, and obtain Rindler modes that can be compared with the entanglement spectrum. 

We make connections of these approximations of Lorentz boosts with the corner transfer matrices in integrable models, and comment on the discrete realization of the Reeh-Schlieder theorem that governs entanglement in a Hilbert space with lower bounded energy. 

Three dimensional fracton phases are new type of phases featuring exotic excitations called fractons. They are gapped point-like excitations constrained to move in sub-dimensional space. In this talk, I will present the gapped fracton topological order discovered in exact solvable models and gapless fracton phase described by U(1) symmetric tensor gauge theories. Their relation with ordinary topological ordered phase would be discussed in detail. Particularly, the fracton topological order exhibited in an exact solvable model called X-cube model can be constructed by coupling toric code layers. And it can also be obtained from a particular rank-2 symmetric tensor gauge theory called scalar charge theory by Higgs mechanism and partial confinement transition.