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

Fermion Condensation in Finite Systems

M. Ya. Amusia, Konstantin G. Popov, Vasily R. Shaginyan +1 more

Springer series in solid-state sciencesOct 25, 20141 citation

Quartet condensation of fermions

Aseem Talukdar

Bulletin of the American Physical SocietyMar 15, 20061 citation

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

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

Abstract 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.Abstract 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.

Nature CommunicationsApr 4, 20254 citations

Spin-1 ladder: A bosonization study

D. Allen, David Sénéchal

We construct a field-theoretic description of two coupled spin-1 Heisenberg chains, starting with the known representation of a single spin-1 chain in terms of Majorana fermions (or Ising models). After reexamining the bosonization rules for two Ising models, taking particular care of order and disorder operators, we obtain a bosonic description of the spin-1 ladder. From renormalization-group and mean-field arguments, we conclude that, for a small interchain coupling, the spin-1 ladder is approximately described by three decoupled, two-frequency sine-Gordon models. We then predict that, starting with decoupled chains, the spin gap decreases linearly with interchain coupling, in both the ferromagnetic and antiferromagnetic directions. Finally, we discuss the possibility of an incommensurate phase in the spin-1 zigzag chain.We construct a field-theoretic description of two coupled spin-1 Heisenberg chains, starting with the known representation of a single spin-1 chain in terms of Majorana fermions (or Ising models). After reexamining the bosonization rules for two Ising models, taking particular care of order and disorder operators, we obtain a bosonic description of the spin-1 ladder. From renormalization-group and mean-field arguments, we conclude that, for a small interchain coupling, the spin-1 ladder is approximately described by three decoupled, two-frequency sine-Gordon models. We then predict that, starting with decoupled chains, the spin gap decreases linearly with interchain coupling, in both the ferromagnetic and antiferromagnetic directions. Finally, we discuss the possibility of an incommensurate phase in the spin-1 zigzag chain.

arXiv:cond-mat/9908224Physical review. B, Condensed matterMay 1, 200031 citations

Quantum field theory for condensation of bosons and fermions

Adriano N. De Souza, Victo S. Filho

AIP conference proceedingsJan 1, 20130 citations

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.