arXiv subjects

Si Min Chan

Publications and source records attributed to Si Min Chan.

5 recordsLinked to original sources

arXiv2026

SMT-AD: a scalable quantum-inspired anomaly detection approach

Quantum-inspired tensor networks algorithms have shown to be effective and efficient models for machine learning tasks, including anomaly detection. Here, we propose a highly parallelizable quantum-inspired approach which we call SMT-AD from Superposition of Multiresolution Tensors for Anomaly Detection. It is based upon the superposition of bond-dimension-1 matrix product operators to transform the input data with Fourier-assisted feature embedding, where the number of learnable parameters grows linearly with feature size, embedding resolutions, and the number of additional components in the matrix product operators structure. We demonstrate successful anomaly detection when applied to standard datasets, including credit card transactions, and find that, even with minimal configurations, it achieves competitive performance against established anomaly detection baselines. Furthermore, it provides a straightforward way to reduce the weight of the model and even improve the performance by highlighting the most relevant input features.

cs.LG↗

arXiv2025

Disorder and the Robustness of Superconductivity on the Flat Band

We study the interplay between on-site disorder and fermion pairing on the quasi one-dimensional flat band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat band superconductivity is robust against disorder: The critical disorder strength, $W_c$, required to localize the fermion pairs and destroy superconductivity, is finite at any interaction strength, $U$, and is proportional to the superconducting weight, $D_s$, of the clean system. Using large scale density matrix renormalization group computations, we show that this transition is of the BKT form. In addition, even at very small interaction strength, the localization is not due to single fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that $W_c$ can be accurately determined by using an appropriate scaling function.

cond-mat.supr-con↗

arXiv2023

Superconductivity with Wannier-Stark Flat Bands

We investigate superconducting transport in the DC field induced Wannier-Stark flat bands in the presence of interactions. Flat bands offer the possibility of unconventional high temperature superconductivity, where the superfluid weight, $D_s$, is enhanced by the density overlap of the localized states. However, construction of flat bands typically requires very precise tuning of Hamiltonian parameters. To overcome this difficulty, we propose a feasible alternative to realize flat bands by applying a DC field in a commensurate lattice direction. We systematically characterize the superconducting behavior on these flat bands by studying the effect of the DC field and attractive Hubbard interaction strengths on the wavefunction, correlation length, pairing order parameter and the superfluid weight $D_s$. Our main result is that the superfluid weight is dramatically enhanced at an optimal value of the interaction strength and weak DC fields.

cond-mat.supr-con↗

arXiv2022

Designer Flat Bands: Topology and Enhancement of Superconductivity

We construct quasi one-dimensional topological and non-topological three-band lattices with tunable band gap and winding number of the flat band. Using mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We show excellent agreement between MF and DMRG. When a phase twist is applied on the system, a phase difference appears between pairing order parameters on different sublattices, and this plays a very important role in the SC density. The SC weight, $D_s$, on the gapped topological, $W\neq0$, flat band increases linearly with interaction strength, $U$, for low values, and with a slope that depends on the details of the compact localized state at $U=0$. As $U\to 0$ for the gapped non-topological flat band ($W=0$), $D_s$ decays with a power law faster than quadratic but slower than exponential. This indicates that isolated non-topological flat bands are less beneficial to SC. In the gapless case (flat band touching the band above it), we find at low $U$ (both for $W=0$ and $W\neq 0$) that $D_s\propto U^φ$ with $φ<1$ contrary to the $U{\rm ln}\, ({\rm const.}/U)$ behavior reported in the literature. In other words, $D_s$ increases faster than linearly for low $U$ thus favoring SC at weak interaction more than the gapped case. For systems with touching bands, we observe that the one-body correlation length, $ξ$, diverges as a power law as $U\rightarrow0$, while for the isolated flat band $ξ(U\to 0)$ is a constant smaller than one lattice spacing. Both behaviors are distinct from the exponential divergence of $ξ$ in the dispersive case. Our results re-establish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.

cond-mat.supr-con↗

arXiv2021

Pairing and superconductivity in quasi one-dimensional flat band systems: Creutz and sawtooth lattices

We study the pairing and superconducting properties of the attractive Hubbard model in two quasi one-dimensional topological lattices: the Creutz and sawtooth lattices. They share two peculiar properties: each of their band structures exhibits a flat band with a non-trivial winding number. The difference, however, is that only the Creutz lattice is genuinely topological, owing to a chiral (sub-lattice) symmetry, resulting in a quantized winding number and zero energy edge modes for open boundary conditions. We use mean field and exact density matrix renormalization group in our work. Our three main results are: (a) For both lattice systems, the superconducting weight, $D_s$, is linear in the coupling strength, $U$, for low values of $U$; (b) for small $U$, $D_s$ is proportional to the quantum metric for the Creutz system but not for the sawtooth system because its sublattices are not equivalent; (c) conventional BCS mean field is not appropriate for such systems with inequivalent sublattices. We show that, for a wide range of densities and coupling strengths, these systems are very well described by a full multi-band mean field method where the pairing parameters and the local particle densities on the inequivalent sublattices are variational mean field parameters.

cond-mat.supr-con↗