Disorder operators are a type of non-local observables for quantum many-body systems, measuring the fluctuations of symmetry charges inside a region. It has been shown that disorder operators can reveal global aspects of many-body states that are otherwise difficult to access through local measurements. We study the disorder operator for U(1) (charge or spin) symmetry in two-dimensional Fermi and non-Fermi liquid states, using the multidimensional bosonization formalism. For a region $A$ , the logarithm of the charge disorder parameter in a Fermi liquid with isotropic interactions scales asymptotically as $l_A\ln l_A$ , with $l_A$ being the linear size of the region $A$ . We calculate the proportionality coefficient in terms of Landau parameters of the Fermi liquid theory. We then study models of the Fermi surface coupled to gapless bosonic fields realizing non-Fermi liquid states. In a simple spinless model, where the fermion density is coupled to a critical scalar, we find that at the quantum critical point the scaling behavior of the charge disorder operators is drastically modified to $l_A \ln^2 l_A$ . We also consider the composite Fermi liquid state and argue that the charge disorder operator scales as $l_A$ .Disorder operators are a type of non-local observables for quantum many-body systems, measuring the fluctuations of symmetry charges inside a region. It has been shown that disorder operators can reveal global aspects of many-body states that are otherwise difficult to access through local measurements. We study the disorder operator for U(1) (charge or spin) symmetry in two-dimensional Fermi and non-Fermi liquid states, using the multidimensional bosonization formalism. For a region $A$, the logarithm of the charge disorder parameter in a Fermi liquid with isotropic interactions scales asymptotically as $l_A\ln l_A$, with $l_A$ being the linear size of the region $A$. We calculate the proportionality coefficient in terms of Landau parameters of the Fermi liquid theory. We then study models of the Fermi surface coupled to gapless bosonic fields realizing non-Fermi liquid states. In a simple spinless model, where the fermion density is coupled to a critical scalar, we find that at the quantum critical point the scaling behavior of the charge disorder operators is drastically modified to $l_A \ln^2 l_A$. We also consider the composite Fermi liquid state and argue that the charge disorder operator scales as $l_A$.

arXiv:2404.04334Physical review. B./Physical review. BSep 22, 20253 citations

Measurement protocol for detecting correlated topological insulators in synthetic quantum systems

Yixin Ma, Chao Xu, Shenghan Jiang

Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for both bosonic and fermionic systems. As correlated topological insulators (TI) approach experimental realization in quantum simulators, conventional probes, such as transport measurements, are not easily applicable to these synthetic platforms. In this study, we focus on two examples of correlated TI: a bosonic TI protected by $\mathbb{Z}_2\times U(1)$ symmetry and the fermionic quantum spin Hall insulator protected by time-reversal symmetry. We propose a unified, readily implementable protocol based on measuring the disorder parameter $\langle\exp(\mathrm{i}θ\hat{Q}_A)\rangle$ for a large subregion $A$ , with $\hat{Q}_A$ the total charge operator within $A$ . Our key finding is that this quantity exhibits non-analytical dependence on $θ$ for correlated TI, a signature robust against decoherence. We establish this diagnostic through both numerical simulations and analytical derivations. This protocol is well-suited for implementation on near-term quantum simulation platforms, providing a direct route to experimentally confirm correlated TI.Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for both bosonic and fermionic systems. As correlated topological insulators (TI) approach experimental realization in quantum simulators, conventional probes, such as transport measurements, are not easily applicable to these synthetic platforms. In this study, we focus on two examples of correlated TI: a bosonic TI protected by $\mathbb{Z}_2\times U(1)$ symmetry and the fermionic quantum spin Hall insulator protected by time-reversal symmetry. We propose a unified, readily implementable protocol based on measuring the disorder parameter $\langle\exp(\mathrm{i}θ\hat{Q}_A)\rangle$ for a large subregion $A$, with $\hat{Q}_A$ the total charge operator within $A$. Our key finding is that this quantity exhibits non-analytical dependence on $θ$ for correlated TI, a signature robust against decoherence. We establish this diagnostic through both numerical simulations and analytical derivations. This protocol is well-suited for implementation on near-term quantum simulation platforms, providing a direct route to experimentally confirm correlated TI.

cond-mat.str-elCross-listedarXiv:2511.10163Nov 14, 20250 citations

Quantum Monte-Carlo Simulations for Disordered Bose Systems

Nandini Trivedi

Springer proceedings in physicsJan 1, 19930 citations

Lattice bosons in a disordered environment

R. Ramakumar, A. N. Das

Dec 13, 20120 citations

Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems

Springer eBooksJan 1, 2002102 citations

Friedel oscillations induced by nonmagnetic impurities in the two-dimensional Hubbard model

W. Ziegler, H. Endres, Werner R. Hanke

We study the interplay of correlations and disorder using an unrestricted slave-Boson technique in real space. Within the saddle-point approximation, we find Friedel oscillations of the charge density in the vicinity of a single nonmagnetic impurity, in agreement with numerical simulations. The corresponding amplitudes are suppressed by repulsive interactions, while attractive correlations lead to a charge-density-wave enhancement. In addition, we investigate the spatial dependence of the local magnetic moment and the formation of a magnetic state at the impurity site.We study the interplay of correlations and disorder using an unrestricted slave-Boson technique in real space. Within the saddle-point approximation, we find Friedel oscillations of the charge density in the vicinity of a single nonmagnetic impurity, in agreement with numerical simulations. The corresponding amplitudes are suppressed by repulsive interactions, while attractive correlations lead to a charge-density-wave enhancement. In addition, we investigate the spatial dependence of the local magnetic moment and the formation of a magnetic state at the impurity site.

arXiv:cond-mat/9704193Physical review. B, Condensed matterAug 15, 19989 citations

A

, the logarithm of the charge disorder parameter in a Fermi liquid with isotropic interactions scales asymptotically as

l_A\ln l_A

, with

l_A

being the linear size of the region

A

. We calculate the proportionality coefficient in terms of Landau parameters of the Fermi liquid theory. We then study models of the Fermi surface coupled to gapless bosonic fields realizing non-Fermi liquid states. In a simple spinless model, where the fermion density is coupled to a critical scalar, we find that at the quantum critical point the scaling behavior of the charge disorder operators is drastically modified to

l_A \ln^2 l_A

. We also consider the composite Fermi liquid state and argue that the charge disorder operator scales as

l_A

\mathbb{Z}_2\times U(1)

symmetry and the fermionic quantum spin Hall insulator protected by time-reversal symmetry. We propose a unified, readily implementable protocol based on measuring the disorder parameter

\langle\exp(\mathrm{i}θ\hat{Q}_A)\rangle

for a large subregion

A

, with

\hat{Q}_A

the total charge operator within

A

. Our key finding is that this quantity exhibits non-analytical dependence on

θ

for correlated TI, a signature robust against decoherence. We establish this diagnostic through both numerical simulations and analytical derivations. This protocol is well-suited for implementation on near-term quantum simulation platforms, providing a direct route to experimentally confirm correlated TI.