Boundary transfer matrix spectrum of measurement-induced transitions

TL;DR

This paper introduces a transfer matrix method to analyze the boundary spectrum of non-unitary conformal field theories describing measurement-induced phase transitions, providing a new systematic numerical tool for studying these complex quantum phenomena.

Contribution

The paper develops a transfer matrix approach to study boundary spectra in MIPTs, applicable to various models including Haar, Clifford circuits, and the measurement-only Ising model, with analytical and numerical results.

Findings

Numerical transfer matrix method effectively characterizes boundary spectra.

Analytical boundary scaling dimensions derived for the measurement-only Ising model.

The approach offers a systematic way to study non-unitary CFTs in quantum measurement contexts.

Abstract

Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum trajectories, are described by boundary observables in this CFT. We introduce a transfer matrix approach to study the boundary spectrum of this field theory, and consider a variety of boundary conditions. We apply this approach numerically to monitored Haar and Clifford circuits, and to the measurement-only Ising model where the boundary scaling dimensions can be derived analytically. Our transfer matrix approach provides a systematic numerical tool to study the spectrum of MIPTs.