Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach

We present a quantum Monte Carlo-based approach to detect and compute the most dominant correlations for many-body systems without prior knowledge. It is based on the measurement and analysis of the correlation density matrix between two (small) subsystems embedded in the full (large) sample. In order to benchmark this procedure, we investigate zero-temperature quantum phase transitions in one- and two-dimensional quantum Ising model as well as the two-dimensional bilayer Heisenberg antiferromagnet. The method paves the way for a systematic identification of unknown or exotic order parameters in unexplored phases on large systems accessible to quantum Monte Carlo methods.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-07-29

• Fields of study

  Physics

• Identifiers
  arXiv 2507.21697
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Detecting the Emergent Continuous Symmetry of Criticality via a Subsystem's Entanglement Spectrum.

  2025cited by this paper
• Bootstrapping the 3d Ising stress tensor

  2024cited by this paper
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian

  2023cited by this paper
• Detecting hidden order in fractional Chern insulators

  2023cited by this paper
• On scientific understanding with artificial intelligence

  2022cited by this paper
• Worm-algorithm-type simulation of the quantum transverse-field Ising model

  2020cited by this paper
• Conformal Fields and Operator Product Expansion in Critical Quantum Spin Chains.

  2019cited by this paper
• Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination.

  2017cited by this paper
• Machine Learning Topological Invariants with Neural Networks

  2017cited by this paper
• Quantum Spin Liquid with Even Ising Gauge Field Structure on Kagome Lattice.

  2017cited by this paper
• Learning phase transitions by confusion

  2016cited by this paper
• The lightcone bootstrap and the spectrum of the 3d Ising CFT

  2016cited by this paper
• Colloquium : Zoo of quantum-topological phases of matter

  2016cited by this paper
• Machine learning phases of matter

  2016cited by this paper
• Construct order parameters from the reduced density matrix spectra

  2013cited by this paper
• Everything you wanted to know about Data Analysis and Fitting but were afraid to ask

  2012cited by this paper
• Colloquium: Hidden order, superconductivity, and magnetism: The unsolved case of URu 2 Si 2

  2011cited by this paper
• Bayesian inference in the scaling analysis of critical phenomena.

  2011cited by this paper
• Uncovering the Physics of Frustrated Quantum Magnets using the Correlation Density Matrix Approach

  2010cited by this paper
• Correlation density matrices for one-dimensional quantum chains based on the density matrix renormalization group

  2009cited by this paper
• Correlation density matrix : an unbiased analysis of exact diagonalizations

  2008cited by this paper
• Unusual liquid state of hard-core bosons on the pyrochlore lattice.

  2007cited by this paper
• Statistical physics of fields

  2007cited by this paper
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers

  2005cited by this paper
• Systematic derivation of order parameters through reduced density matrices.

  2005cited by this paper
• Many-body density matrices on a two-dimensional square lattice: Noninteracting and strongly interacting spinless fermions

  2005cited by this paper
• Detecting topological order in a ground state wave function.

  2005cited by this paper
• Topological entanglement entropy.

  2005cited by this paper
• Stochastic series expansion method for quantum Ising models with arbitrary interactions.

  2003cited by this paper
• Pyrochlore photons: The U ( 1 ) spin liquid in a S = 1 2 three-dimensional frustrated magnet

  2003cited by this paper
• Quantum Entanglement in Condensed Matter Systems

  2002cited by this paper
• Fractionalization in an easy-axis Kagome antiferromagnet

  2001cited by this paper
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class

  2001cited by this paper
• Stochastic series expansion method with operator-loop update

  1999cited by this paper
• The loop algorithm

  1997cited by this paper
• Conformal Field Theory.

  1992cited by this paper
• Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains.

  1989cited by this paper
• Field theory

  1979cited by this paper
• More is different.

  1972cited by this paper
• Two Soluble Models of an Antiferromagnetic Chain

  1961cited by this paper
• Antiferromagnetism

  1955cited by this paper

• Two-site entanglement in the two-dimensional Hubbard model

  2025cites this paper
• Mixed-State Measurement-Induced Phase Transitions in Imaginary-Time Dynamics

  2025cites this paper