@article {2945, title = {Chiral central charge from a single bulk wave function}, journal = {Phys. Rev. Lett. }, volume = {128}, year = {2022}, month = {4/28/2022}, pages = {176402}, abstract = {

A (2+1)-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity associated with the effective field theory of the edge. We derive a formula for the chiral central charge that, akin to the topological entanglement entropy, is completely determined by the many-body ground state wave function in the bulk. According to our formula, nonzero chiral central charge gives rise to a topological obstruction that prevents the ground state wave function from being real-valued in any local product basis.

}, doi = {10.1103/PhysRevLett.128.176402}, url = {https://arxiv.org/abs/2110.06932}, author = {Isaac H. Kim and Bowen Shi and Kohtaro Kato and Victor V. Albert} } @article {3132, title = {Modular commutator in gapped quantum many-body systems}, journal = {Physical Review B}, volume = {106}, year = {2022}, month = {8/26/2022}, abstract = {

In arXiv:2110.06932, we argued that the chiral central charge -- a topologically protected quantity characterizing the edge theory of a gapped (2+1)-dimensional system -- can be extracted from the bulk by using an order parameter called the modular commutator. In this paper, we reveal general properties of the modular commutator and strengthen its relationship with the chiral central charge. First, we identify connections between the modular commutator and conditional mutual information, time reversal, and modular flow. Second, we prove, within the framework of the entanglement bootstrap program, that two topologically ordered media connected by a gapped domain wall must have the same modular commutator in their respective bulk. Third, we numerically calculate the value of the modular commutator for a bosonic lattice Laughlin state for finite sizes and extrapolate to the infinite-volume limit. The result of this extrapolation is consistent with the proposed formula up to an error of about 0.7\%.

}, doi = {10.1103/physrevb.106.075147}, url = {https://arxiv.org/abs/2110.10400}, author = {Isaac H. Kim and Bowen Shi and Kohtaro Kato and Victor V. Albert} } @article {2101, title = {Robust entanglement renormalization on a noisy quantum computer}, year = {2017}, month = {2017/11/20}, abstract = {

A method to study strongly interacting quantum many-body systems at and away from criticality is proposed. The method is based on a MERA-like tensor network that can be efficiently and reliably contracted on a noisy quantum computer using a number of qubits that is much smaller than the system size. We prove that the outcome of the contraction is stable to noise and that the estimated energy upper bounds the ground state energy. The stability, which we numerically substantiate, follows from the positivity of operator scaling dimensions under renormalization group flow. The variational upper bound follows from a particular assignment of physical qubits to different locations of the tensor network plus the assumption that the noise model is local. We postulate a scaling law for how well the tensor network can approximate ground states of lattice regulated conformal field theories in d spatial dimensions and provide evidence for the postulate. Under this postulate, a O(logd (1/δ))-qubit quantum computer can prepare a valid quantum-mechanical state with energy density δ above the ground state. In the presence of noise, δ = O( logd+1(1/)) can be achieved, where  is the noise strength.

}, url = {https://arxiv.org/abs/1711.07500}, author = {Isaac H. Kim and Brian Swingle} }