arXiv subjects

Ruoshui Wang

Publications and source records attributed to Ruoshui Wang.

5 recordsLinked to original sources

arXiv2022

Virasoro Generators in the Fibonacci Model Tensor Network -- Tackling Finite Size Effects

In this paper, we extend the method implementing Virasoro operators in a tensor network we proposed in arXiv:2205.04500 and test it on the Fibonacci model, which is known to suffer from far more finite size effects. To pick up the "seed" state that would flow to the stress tensor in the thermodynamic limit, we make use of the topological idempotent that projects the transfer matrix to the trivial sector. Combined with an optimization method, the seed state can be identified. We demonstrate that the descendant states in the Fibonacci model can be correctly generated with this approximate stress tensor, giving further evidence that the method applies more generally.

cond-mat.str-el↗

arXiv2022

CFT$_D$ from TQFT$_{D+1}$ via Holographic Tensor Network, and Precision Discretisation of CFT$_2$

We show that the path-integral of conformal field theories in $D$ dimensions (CFT$_D$) can be constructed by solving for eigenstates of an RG operator following from the Turaev-Viro formulation of a topological field theory in $D+1$ dimensions (TQFT$_{D+1}$), explicitly realising the holographic sandwich relation between a symmetric theory and a TQFT. Generically, exact eigenstates corresponding to symmetric-TQFT$_D$ follow from Frobenius algebra in the TQFT$_{D+1}$. For $D=2$, we constructed eigenstates that produce 2D rational CFT path-integral exactly, which, curiously connects a continuous field theoretic path-integral with the Turaev-Viro state sum. We also devise and illustrate numerical methods for $D=2,3$ to search for CFT$_D$ as phase transition points between symmetric TQFT$_D$. Finally since the RG operator is in fact an exact analytic holographic tensor network, we compute ``bulk-boundary'' correlator and compare with the AdS/CFT dictionary at $D=2$. Promisingly, they are numerically compatible given our accuracy, although further works will be needed to explore the precise connection to the AdS/CFT correspondence.

hep-th↗

arXiv2022

Bang-bang algorithms for quantum many-body ground states: a tensor network exploration

We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H = H_A + H_B$ in infinite systems. The first algorithm is a generalization of the quantum approximate optimization algorithm (QAOA) and uses a quantum computer to evolve an initial product state into an approximation of the ground state of $H$, by alternating between $H_A$ and $H_B$. We show for the 1D quantum Ising model that the accuracy in representing a gapped ground state improves exponentially with the number of alternations. The second algorithm is the variational imaginary time ansatz (VITA), which uses a classical computer to simulate the ground state via alternating imaginary time steps with $H_A$ and $H_B$. We find for the 1D quantum Ising model that an accurate approximation to the ground state is obtained with a total imaginary time $\tau$ that grows only logarithmically with the inverse energy gap $1/ \Delta$ of $H$. This is much faster than imaginary time evolution by $H$, which would require $\tau \sim 1/ \Delta$.

cond-mat.str-el↗

arXiv2022

Emergence of Kac-Moody Symmetry in Critical Quantum Spin Chains

Given a critical quantum spin chain with a microscopic Lie-group symmetry, corresponding e.g. to $U(1)$ or $SU(2)$ spin isotropy, we numerically investigate the emergence of Kac-Moody symmetry at low energies and long distances. In that regime, one such critical quantum spin chain is described by a conformal field theory where the usual Virasoro algebra associated to conformal invariance is augmented with a Kac-Moody algebra associated to conserved currents. Specifically, we first propose a method to construct lattice operators corresponding to the Kac-Moody generators. We then numerically show that, when projected onto low energy states of the quantum spin chain, these operators indeed approximately fulfill the Kac-Moody algebra. The lattice version of the Kac-Moody generators allow us to compute the so-called level constant and to organize the low-energy eigenstates of the lattice Hamiltonian into Kac-Moody towers. We illustrate the proposal with the XXZ model and the Heisenberg model with a next-to-nearest-neighbor coupling.

cond-mat.str-el↗

arXiv2022

Virasoro and Kac-Moody algebra in generic tensor network representations of 2d critical lattice partition functions

In this paper, we propose a general implementation of the Virasoro generators and Kac-Moody currents in generic tensor network representations of 2-dimensional critical lattice models. Our proposal works even when a quantum Hamiltonian of the lattice model is not available, which is the case in many numerical computations involving numerical blockings. We tested our proposal on the 2d Ising model, and also the dimer model, which works to high accuracy even with a fairly small system size. Our method makes use of eigenstates of a small cylinder to generate descendant states in a larger cylinder, suggesting some intricate algebraic relations between lattice of different sizes.

cond-mat.str-el↗