Density-Matrix Mean-Field Theory

Abstract

Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean-field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.

Published version in SciPost Physics, and mentioned in SciPost Selections

References in corpus (11)

• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• A Short Introduction to Numerical Linked-Cluster Expansions
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Critical magnetization behaviors of the triangular and Kagome lattice quantum antiferromagnets
• The phase diagram of the antiferromagnetic XXZ model on the triangular lattice
• Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective
• Phase Diagram of Triangular Lattice Quantum Ising Model under External Field
• Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice