6 papers
Structure of matrix product locally purifiable density operators
Yale Yauk, Yuhan Liu, Ignacio Cirac
Tensor network methods provide powerful analytical and numerical tools for characterizing quantum phases of matter. While the mathematical structure of matrix product states (MPS)…
Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
Denise Cocchiarella, Mingru Yang, Yueshui Zhang +3
Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors o…
Polynomial-time certification of fidelity for many-body mixed states and mixed-state universality classes
Yuhan Liu, Yijian Zou
Computation of Uhlmann fidelity between many-body mixed states generally involves full diagonalization of exponentially large matrices. In this work, we introduce a polynomial-time…
Parent Lindbladians for Matrix Product Density Operators
Yuhan Liu, Alberto Ruiz-de-Alarcón, Georgios Styliaris +3
Understanding quantum phases of matter is a fundamental goal in physics. For pure states, the representatives of phases are the ground states of locally interacting Hamiltonians, w…
Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries
Yuhan Liu, Andras Molnar, Xiao-Qi Sun +3
Despite recent advances in the lattice representation theory of (generalized) symmetries, many simple quantum spin chains of physical interest are not included in the rigid framewo…
On the Chow Rings of the Moduli Spaces and
Yuhan Liu
In this paper we prove that the rational Chow rings of and are tautological, and that these moduli spaces have the Chow Künneth generation…