TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.4.142
TI  - Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
PY  - 2025/04/29
UR  - https://scipost.org/SciPostPhys.18.4.142
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 4
SP  - 142
A1  - Schneider, Jan Thorben
AU  - Ueda, Atsushi
AU  - Liu, Yifan
AU  - Läuchli, Andreas
AU  - Oshikawa, Masaki
AU  - Tagliacozzo, Luca
AB  - We set up an effective field theory formulation for the renormalization flow of matrix product states (MPS) with finite bond dimension, focusing on systems exhibiting finite-entanglement scaling close to a conformally invariant critical fixed point. We show that the finite MPS bond dimension $\chi$ is equivalent to introducing a perturbation by a relevant operator to the fixed-point Hamiltonian. The fingerprint of this mechanism is encoded in the $\chi$-independent universal transfer matrix's gap ratios, which are distinct from those predicted by the unperturbed Conformal Field Theory (CFT). This phenomenon defines a renormalization group self-congruent point, where the relevant coupling constant ceases to flow due to a balance of two effects; When increasing $\chi$, the infrared scale, set by the correlation length $\xi(\chi)$, increases, while the strength of the perturbation at the lattice scale decreases. The presence of a self-congruent point does not alter the validity of the finite-entanglement scaling hypothesis, since the self-congruent point is located at a finite distance from the critical fixed point, well inside the scaling regime of the CFT. We corroborate this framework with numerical evidence from the exact solution of the Ising model and density matrix renormalization group (DMRG) simulations of an effective lattice model.
ER  -

@Article{10.21468/SciPostPhys.18.4.142,
	title={{Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling}},
	author={Jan T. Schneider and Atsushi Ueda and Yifan Liu and Andreas M. Läuchli and Masaki Oshikawa and Luca Tagliacozzo},
	journal={SciPost Phys.},
	volume={18},
	pages={142},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.4.142},
	url={https://scipost.org/10.21468/SciPostPhys.18.4.142},
}