SineKAN, a Kolmogorov-Arnold network with sinusoidal activations, accurately represents ground states of 1D spin chains and outperforms RBM, LSTM, and MLP neural quantum states in the J1-J2 model.
Multi-Chain Mean-Field Theory of Quasi One-Dimensional Quantum Spin Systems
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abstract
A multi-chain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C_0 is modeled by a number of neighbor chains C_d, d = +/-1,...,+/-n, with the edge chains (d=+/-n) coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1)-chain Hamiltonian is solved self-consistently for $n$ up to 4. The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings alpha behaves as M=A*alpha^1/2 enhanced by a multiplicative logarithmic correction.
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Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States
SineKAN, a Kolmogorov-Arnold network with sinusoidal activations, accurately represents ground states of 1D spin chains and outperforms RBM, LSTM, and MLP neural quantum states in the J1-J2 model.