This series consists of talks in the area of Condensed Matter.
A featureless insulator is a gapped phase of matter that does not exhibit fractionalization or other exotic physics, and thus has a unique ground state. The classic albeit non-interacting example is an electronic band insulator. A standard textbook argument tells us that band insulators require an even number of electrons -- an integer number for each spin -- per unit cell.
I will discuss the violation of spin-charge separation in generic Luttinger liquids and investigate its effect on the relaxation, thermal and electrical transport of genuine spin-1/2 electron liquids in ballistic quantum wires. We will identify basic scattering processes compatible with the symmetry of the problem and conservation laws that lead to the decay of plasmons into the spin modes and also discuss Brownian backscattering of spin excitations.
I will discuss the violation of spin-charge separation in generic Luttinger liquids and investigate its effect on the relaxation, thermal and electrical transport of genuine spin-1/2 electron liquids in ballistic quantum wires. We will identify basic scattering processes compatible with the symmetry of the problem and conservation laws that lead to the decay of plasmons into the spin modes and also discuss Brownian backscattering of spin excitations.
We construct a model which realizes a (3+1)-dimensional symmetry-protected topological phase of bosons with U(1) charge conservation and time reversal symmetry, envisioned by A. Vishwanath and T. Senthil [PRX 4 011016]. Our model works by introducing an additional spin degree of freedom, and binding its hedgehogs to a species of charged bosons. We study the model using Monte Carlo and determine its bulk phase diagram; the phase where the bound states of hedgehogs and charges condense is the topological phase, and we demonstrate this by observing a Witten effect.
A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we demonstrate that the ground state of a topological phase itself encodes critical properties of its transition to a trivial phase. To extract this information, we introduce a partition of the system into two subsystems both of which extend throughout the bulk in all directions.
We show that for a system evolving unitarily under a stochastic quantum circuit, the notions of irreversibility, universality of computation, and entanglement are closely related. As the state of the system evolves from an initial product state, it becomes increasingly entangled until entanglement reaches a maximum. We define irreversibility as the failure to find a circuit that disentangles a maximally entangled state.
We discuss properties of 2-point functions in CFTs in 2+1D at finite temperature. For concreteness, we focus on those involving conserved flavour currents, in particular on the associated conductivity. At frequencies much greater than the temperature, ω >> T, the ω dependence of the conductivity can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation value at T > 0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT.
In the last few decades, substantial advances have been made in our ability to make general statements about the thermodynamics of systems driven far from thermal equilibrium. In this talk, I will give a brief overview of some the most basic results in this area and explain their connection to classic results in linear response theory.
We show that the numerical strong disorder renormalization group algorithm (SDRG) of Hikihara et.\ al.\ [{Phys. Rev. B} {\bf 60}, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions and the entanglement entropy using the geometrical properties of the TTN.
This has been a leading question in condensed matter physics since the discovery of the cuprate superconductors. In this talk I will review some of the DMRG and tensor network results for the ground states of these models. A key question I'll address is the issue of stripes: are the ground states striped? Do stripes compete with or induce d-wave superconductivity? Another question I'll address is: how well does 2D DMRG do in comparison with iPEPS and quantum Monte Carlo. I will also show recent results for a standard 3-band Hubbard model for the cuprates.