THEORETICAL PHYSICIST

Racah Institute of Physics, Hebrew University of Jerusalem

# Erez Zohar

Spring Semster, 2020 and 2021:

Quantum Information Methods

for Many-Body Physics

Quantum Many Body Physics is a very challenging research field, that requires the development of new computation methods, for handling strong interaction and non-pertubative models. The course will introduce two modern approaches to many-body physics and quantum field theory, rooted in quantum information theory: one is quantum simulation – mapping one quantum system to another one which is controllable in the laboratory, and tensor networks, which allow one to perform efficient calculations for physically relevant many body quantum states. The course will include examples from both condensed matter and particle physics (prior knowledge with the demonstrated models is not required).

Topics to be covered:

1. Introduction: review of second quantization of bosons and fermions; Symmetries (global and local), conserved quantities, constraints; Demonstrating system (that will be useful in the next section): ultracold atoms in optical lattice and Hubbard models

2. Hamiltonians on demand - quantum simulators: Motivation; Analog simulation, imposing symmetries, theory of effective Hamiltonians, state preparation, adiabatic evolution; Digital simulation, the Trotter-Suzuki approximation of time evolution, tailoring many body interactions from two-body interactions with ancillas.

3. States on demand - tensor network states: Non interacting Hamiltonians, Gaussian states; Local interacting Hamiltonians and entanglement area law; Motivation for tensor networks as physically relevant states, a brief overview of tensor network constructions (PEPS, MPS, MERA, ...) ; PEPS (Projected Entangled Pair States) and their 1d version, MPS (Matrix Product States): structure and construction, basic properties, imposing symmetries on demand, parent Hamiltonians and analytical properties; Fermionic PEPS

Links to the Hebrew University Coures Catalogue:

The course material is accessible to Hebrew University Students via moodle.huji.ac.il.