Contributor info: Prof. Michael Hermele

Xie Chen, Michael Hermele, David T. Stephen

SciPost Phys. 19, 107 (2025) · published 23 October 2025 | Toggle abstract · pdf

In previous work, it was shown that non-trivial gapped states can be generated from a product state using a sequential quantum circuit. Explicit circuit constructions were given for a variety of gapped states at exactly solvable fixed points. In this paper, we show that a similar generation procedure can be established for chiral topological states as well, despite the fact that they lack a zero-correlation-length exactly solvable form. Instead of sequentially applying local unitary gates, we sequentially evolve the Hamiltonian by changing local terms in one subregion and then the next. The Hamiltonian remains gapped throughout the process, giving rise to an adiabatic evolution mapping the ground state from a product state to a chiral topological state. We demonstrate such a sequential adiabatic generation process for free fermion chiral states like the Chern Insulator and the $p+ip$ superconductor. Moreover, we show that coupling a quantum state to a discrete gauge group can be achieved through a sequential quantum circuit, thereby generating interacting chiral topological states from the free fermion ones.

Marvin Qi, David T. Stephen, Xueda Wen, Daniel Spiegel, Markus J. Pflaum, Agnès Beaudry, Michael Hermele

SciPost Phys. 18, 168 (2025) · published 28 May 2025 | Toggle abstract · pdf

We employ matrix product states (MPS) and tensor networks to study topological properties of the space of ground states of gapped many-body systems. We focus on families of states in one spatial dimension, where each state can be represented as an injective MPS of finite bond dimension. Such states are short-range entangled ground states of gapped local Hamiltonians. To such parametrized families over $X$ we associate a gerbe, which generalizes the line bundle of ground states in zero-dimensional families (\textit{i.e.} in few-body quantum mechanics). The nontriviality of the gerbe is measured by a class in $H^3(X, \Z)$, which is believed to classify one-dimensional parametrized systems. We show that when the gerbe is nontrivial, there is an obstruction to representing the family of ground states with an MPS tensor that is continuous everywhere on $X$. We illustrate our construction with two examples of nontrivial parametrized systems over $X=S^3$ and $X = \R P^2 × S^1$. Finally, we sketch using tensor network methods how the construction extends to higher dimensional parametrized systems, with an example of a two-dimensional parametrized system that gives rise to a nontrivial 2-gerbe over $X = S^4$.