A real space decoupling transformation for quantum many-body systems

Abstract

We propose a real space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of [Phys. Rev. Lett. 99, 220405 (2007)], the key ingredient of this decoupling transformation is the concept of entanglement renormalization, or removal of short-range entanglement. We demonstrate the feasibility of the approach, both analytically and numerically, by decoupling in real space the ground state of a critical quantum spin chain into two. Generalized notions of RG flow and of scale invariance are also put forward.

5 pages, 6 figures, includes appendix

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• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Probing spin-charge separation in a Tomonaga-Luttinger liquid
• Entanglement renormalization, scale invariance, and quantum criticality
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