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A universal description of Mott insulators: Characterizing quantum phases beyond broken symmetries

Matheus de Sousa, Zhiyu Fan, Wei Ku

Abstract

Using Mott insulators as a prototypical example, we demonstrate a dynamics-based characterization of quantum phases of matter through a general N-body renormalization group framework. The essential "Mott-ness" turns out to be characterized by a change of size-scaling of the effective intra- momentum repulsions between long-lived emergent "eigen-particles" that encodes the dynamics of two-body bound states in the high-energy sector. This directly offers a universal characterization at long space-time scale for the corresponding class of Mott insulators through a uniform single occupation of all momenta, and otherwise Mott metals. This universal description naturally paves the way to topological Mott insulators and is straightforward to extend to bosonic Mott systems. More generally, this demonstration exemplifies a generic paradigm of characterizing quantum phases of matter through their distinct dynamics beyond broken symmetries.

A universal description of Mott insulators: Characterizing quantum phases beyond broken symmetries

Abstract

Using Mott insulators as a prototypical example, we demonstrate a dynamics-based characterization of quantum phases of matter through a general N-body renormalization group framework. The essential "Mott-ness" turns out to be characterized by a change of size-scaling of the effective intra- momentum repulsions between long-lived emergent "eigen-particles" that encodes the dynamics of two-body bound states in the high-energy sector. This directly offers a universal characterization at long space-time scale for the corresponding class of Mott insulators through a uniform single occupation of all momenta, and otherwise Mott metals. This universal description naturally paves the way to topological Mott insulators and is straightforward to extend to bosonic Mott systems. More generally, this demonstration exemplifies a generic paradigm of characterizing quantum phases of matter through their distinct dynamics beyond broken symmetries.
Paper Structure (5 sections, 1 theorem, 27 equations, 1 figure, 1 table)

This paper contains 5 sections, 1 theorem, 27 equations, 1 figure, 1 table.

Table of Contents

  1. Mott Transition to Mott semimetal
  2. Unitary Transformation for the Fourier Transform
  3. Order-by-order diagonalization
  4. Unitary transformation to absorb intersite charge fluctuation: c†ᵢσ → ĉ†ᵢσ
  5. Unitary transformation toward fix points of long space-time scale: ĉ†ᵢσ → c̃†ᵢσ

Key Result

Theorem 1

The resulting normal ordered terms of a commutator, $[A_1,A_2]$, for normal ordered operators $A_1$ and $A_2$, of $n_1$- and $n_2$-body, respectively, can only be of $m$-body with $m\in[\max\{n_1,n_2\}, n_1+n_2-1]$.

Figures (1)

  • Figure 1: Schematics of eigen-particle occupation in several quantum phases. (a) Double occupation (in red) of all momenta in band insulators. (b) Double occupation within Fermi wavevector ($k<k_F$) in band metals. (c) Compensating number of zero and double occupations in Mott-semimetals. (d) Single occupation (in blue) of all momenta in Mott insulators. (e) Double occupation in few momenta in Mott-metals. For easier visualization, the dispersions of eigen-particle energy $\braket{\tilde{\epsilon}_k}$ in (c) and (e) are for a reference Mott insulating (excited) state of the system, instead of the metallic ground state.

Theorems & Definitions (1)

  • Theorem : Bound in particle number from commutation