Quantum state, in relativistic quantum mechanics, itself turns out to be an entangled state due to its own degrees freedom such as spin and momentum. This peculiar entanglement leaves the transformed state mixed. We consider the fractional charge state that arises in a theory of fermion interacting with scalar background in this context. The apparent entanglement occurs between fermion ans scalar through Yukawa-type interaction. However, the spontaneous symmetry breaking causes appearance of the $c$ -number zero energy solution of the Dirac equation as a pure state. Quantum entanglement in such relativistic system is proposed to have a microscopic view of the spontaneous symmetry breaking which has been realised in condensed matter system like polyacetylene.Quantum state, in relativistic quantum mechanics, itself turns out to be an entangled state due to its own degrees freedom such as spin and momentum. This peculiar entanglement leaves the transformed state mixed. We consider the fractional charge state that arises in a theory of fermion interacting with scalar background in this context. The apparent entanglement occurs between fermion ans scalar through Yukawa-type interaction. However, the spontaneous symmetry breaking causes appearance of the $c$-number zero energy solution of the Dirac equation as a pure state. Quantum entanglement in such relativistic system is proposed to have a microscopic view of the spontaneous symmetry breaking which has been realised in condensed matter system like polyacetylene.

arXiv:0911.3030Nov 16, 20090 citations

Strong Fermion Interactions in Fractional Quantum Hall States

S. B. Mulay, John J. Quinn, Mark Shattuck

Springer series in solid-state sciencesJan 1, 20180 citations

Composite particle theory of three-dimensional gapped fermionic phases: Fractional topological insulators and charge-loop excitation symmetry

Peng Ye, Taylor L. Hughes, Joseph Maciejko +1 more

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e., the deconfined phase of ${\mathbb{Z}}_{2}$ gauge theory) is a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ Chern-Simons theory in which gauge charges (i.e., $e$ and $m$ particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-H\"uckel--type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and $\mathrm{\ensuremath{\Theta}}\ensuremath{\ne}\ensuremath{\pi}$, the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry ( $\mathsf{Charles}$ ) of 3D Abelian topological phases. We show that line twist defects, which realize $\mathsf{Charles}$ transformations, exhibit non-Abelian fusion properties.Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e., the deconfined phase of ${\mathbb{Z}}_{2}$ gauge theory) is a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ Chern-Simons theory in which gauge charges (i.e., $e$ and $m$ particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-H\"uckel--type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and $\mathrm{\ensuremath{\Theta}}\ensuremath{\ne}\ensuremath{\pi}$, the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry ($\mathsf{Charles}$) of 3D Abelian topological phases. We show that line twist defects, which realize $\mathsf{Charles}$ transformations, exhibit non-Abelian fusion properties.

arXiv:1603.02696Physical review. B./Physical review. BSep 2, 201640 citations

Fingerprints of supersymmetric spin and charge dynamics observed by inelastic neutron scattering

Björn Wehinger, Franco T. Lisandrini, Noam Kestin +12 more

Supersymmetry is an algebraic property of a quantum Hamiltonian that, by giving every boson a fermionic superpartner and vice versa, may underpin physics beyond the Standard Model. Fractional bosonic and fermionic quasiparticles are familiar in condensed matter, as in the spin and charge excitations of the $t$ - $J$ model describing electron dynamics in one-dimensional materials, but this type of symmetry is almost unknown. However, the triplet excitations of a quantum spin ladder in an applied magnetic field provide a supersymmetric analogue of the $t$ - $J$ chain. Here we perform neutron spectroscopy on the spin-ladder compounds (C $_5$ D $_{12}$ N) $_2$ CuBr $_4$ and (C $_5$ D $_{12}$ N) $_2$ CuCl $_4$ over a range of applied fields and temperatures, and apply matrix-product-state methods to the ladder and equivalent chain models. From the momentum-resolved dynamics of a single charge-like excitation in a bath of fractional spins, we find essential differences in thermal broadening between the supersymmetric and non-supersymmetric sectors. The persistence of a strict zone-centre pole at all temperatures constitutes an observable consequence of supersymmetry that marks the beginning of supersymmetric studies in experimental condensed matter.Supersymmetry is an algebraic property of a quantum Hamiltonian that, by giving every boson a fermionic superpartner and vice versa, may underpin physics beyond the Standard Model. Fractional bosonic and fermionic quasiparticles are familiar in condensed matter, as in the spin and charge excitations of the $t$-$J$ model describing electron dynamics in one-dimensional materials, but this type of symmetry is almost unknown. However, the triplet excitations of a quantum spin ladder in an applied magnetic field provide a supersymmetric analogue of the $t$-$J$ chain. Here we perform neutron spectroscopy on the spin-ladder compounds (C$_5$D$_{12}$N)$_2$CuBr$_4$ and (C$_5$D$_{12}$N)$_2$CuCl$_4$ over a range of applied fields and temperatures, and apply matrix-product-state methods to the ladder and equivalent chain models. From the momentum-resolved dynamics of a single charge-like excitation in a bath of fractional spins, we find essential differences in thermal broadening between the supersymmetric and non-supersymmetric sectors. The persistence of a strict zone-centre pole at all temperatures constitutes an observable consequence of supersymmetry that marks the beginning of supersymmetric studies in experimental condensed matter.

arXiv:2408.12626Aug 19, 20240 citations

c

-number zero energy solution of the Dirac equation as a pure state. Quantum entanglement in such relativistic system is proposed to have a microscopic view of the spontaneous symmetry breaking which has been realised in condensed matter system like polyacetylene.

{\mathbb{Z}}_{2}

gauge theory) is a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ Chern-Simons theory in which gauge charges (i.e.,

e

and

m

particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-H\"uckel--type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and $\mathrm{\ensuremath{\Theta}}\ensuremath{\ne}\ensuremath{\pi}$, the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry (

\mathsf{Charles}

) of 3D Abelian topological phases. We show that line twist defects, which realize

\mathsf{Charles}

transformations, exhibit non-Abelian fusion properties.

t

J

model describing electron dynamics in one-dimensional materials, but this type of symmetry is almost unknown. However, the triplet excitations of a quantum spin ladder in an applied magnetic field provide a supersymmetric analogue of the

t

J

chain. Here we perform neutron spectroscopy on the spin-ladder compounds (C

_5

_{12}

_2

CuBr

_4

and (C

_5

_{12}

_2

CuCl

_4

over a range of applied fields and temperatures, and apply matrix-product-state methods to the ladder and equivalent chain models. From the momentum-resolved dynamics of a single charge-like excitation in a bath of fractional spins, we find essential differences in thermal broadening between the supersymmetric and non-supersymmetric sectors. The persistence of a strict zone-centre pole at all temperatures constitutes an observable consequence of supersymmetry that marks the beginning of supersymmetric studies in experimental condensed matter.