I review the basics of the Metropolis algorithm and comment on the infamous “sign problem” affecting most areas of physics. Video. Notes.
Category Archives: Quantum Monte Carlo
Toward QMC: Calculating thermal expectation values
I show the first notions of how to go about calculating thermal expectation values in quantum Monte Carlo. I work out an example for the particle number operator and show expressions for the one-body density matrix. I assume that the field configurations are given. More on how to obtain those samples next time! Video. Notes.
Toward QMC: Spacetime determinant identities
I show how to rewrite the fermionic and bosonic determinants of previous videos in a blown-up spacetime formulation, where the matrices now become sparse and the connections to QFT and entanglement become much more interesting and useful! Check it out. Video. Notes.
Toward QMC: Trace-determinant identities. Part 2.
This is the fourth episode of the “Toward QMC” series. In the previous episode, I started to show how a crucial identity is proven in the case of fermions. Here I give more details on how to carry out that proof for products of multiple operators and explain what happens in the bosonic case. Check …
Continue reading “Toward QMC: Trace-determinant identities. Part 2.”
Toward QMC: Trace-determinant identities. Part 1.
This is the third episode of the “Toward QMC” series. In the previous episode, I brought up a trace-determinant identity without proof. Here I take a big first step to show how that identity is proven in the case of fermions. More on this (including bosons!) in part 2! Video. Notes.
Toward QMC: Hubbard-Stratonovich transformation
This is the second episode of the Toward-QMC series. I discuss how interactions enter the thermodynamics of quantum systems from an operational standpoint. The Hubbard-Stratonovich transformation allows us to take a step forward by decomposing the interaction factor as an integral over external fields. Check it out! More details on the algebra next time.Video. Notes.
Toward QMC: Trotter-Suzuki factorization
Here’s a first installment of an introductory series dedicated to quantum Monte Carlo at finite temperature. First step: a brief technical note on the Trotter-Suzuki factorization. Video. Notes.