Boundary transfer matrix spectrum of measurement-induced transitions

Abhishek Kumar, Kemal Aziz, Ahana Chakraborty, Andreas W.W. Ludwig, Sarang Gopalakrishnan, J. H. Pixley, Romain Vasseur

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Measurement-induced phase transitions (MIPTs) are known to be described by nonunitary 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.

Original languageEnglish (US)
Article number014303
JournalPhysical Review B
Issue number1
StatePublished - Jan 1 2024
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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