Inert States of Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>Systems

Mäkelä, Harri; Suominen, Kalle-Antti

doi:10.1103/physrevlett.99.190408

Cited by 53 publications

(57 citation statements)

References 27 publications

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“…Two kinds of stationary states with residual symmetry exist. Inert states are stationary points of the free energy independent of the precise form of F J [48][49][50][51][52], whereas noninert states depend on the interaction parameters of the energy functional, requiring knowledge of its precise form. Following the method presented in Ref.…”

Section: Phenomenology Of Multicomponent Pairingmentioning

confidence: 99%

“…The chiral pairing states are eigenstates of rotations about the quantization axis with eigenvalue e −iθM . All pairing states given by jJ; Mi have the special property that they are inert states of the free energy [50][51][52]: they are stationary points of the energy independent of its precise form. The states jJ; Mi have a continuous isotropy group, where the isotropy group is defined as the subgroup of total symmetry group G, which leaves the state invariant.…”

Section: A Symmetry Properties and Stationary Pairing Statesmentioning

confidence: 99%

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Pairing States of Spin- 32 Fermions: Symmetry-Enforced Topological Gap Functions

Venderbos¹,

Savary²,

Ruhman³

et al. 2018

Phys. Rev. X

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We study the topological properties of superconductors with paired j ¼ 3 2 quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based half-Heusler materials, which have recently been established as low-temperature and low-carrier density superconductors. Motivated by this experimental observation, we obtain a comprehensive symmetry-based classification of topological pairing states in systems with higher angular momentum Cooper pairing. Our study consists of two main parts. First, we develop the phenomenological theory of multicomponent (i.e., higher angular momentum) pairing by classifying the stationary points of the free energy within a Ginzburg-Landau framework. Based on the symmetry classification of stationary pairing states, we then derive the symmetry-imposed constraints on their gap structures. We find that, depending on the symmetry quantum numbers of the Cooper pairs, different types of topological pairing states can occur: fully gapped topological superconductors in class DIII, Dirac superconductors, and superconductors hosting Majorana fermions. Notably, we find a series of nematic fully gapped topological superconductors, as well as double-and triple-Dirac superconductors, with quadratic and cubic dispersion, respectively. Our approach, applied here to the case of j ¼ 3 2 Cooper pairing, is rooted in the symmetry properties of pairing states, and can therefore also be applied to other systems with higher angular momentum and high-spin pairing. We conclude by relating our results to experimentally accessible signatures in thermodynamic and dynamic probes.

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Section: Phenomenology Of Multicomponent Pairingmentioning

confidence: 99%

Section: A Symmetry Properties and Stationary Pairing Statesmentioning

confidence: 99%

Pairing States of Spin- 32 Fermions: Symmetry-Enforced Topological Gap Functions

Venderbos¹,

Savary²,

Ruhman³

et al. 2018

Phys. Rev. X

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“…results in a change of the symmetry group [105]. Because of the isomorphism between the states of a spin-j particle and the symmetric states of 2 j qubits, this definition can be extended to symmetric n qubit states.…”

Section: Two and Three Qubit Symmetric Statesmentioning

confidence: 99%

“…It has also been used to study Berry phases in high spin systems [100] and quantum chaos [94,101], and it has been put into relation to geometrically motivated SLOCC invariants [61]. Within many-body physics it has been used for finding solutions to the Lipkin-Meshkov-Glick (LMG) model [22], and for studying and identifying phases in spinor Bose-Einstein-condensates [102][103][104][105]. It has also been used to look for optimal resources for reference frame alignment [106], for phase estimation, and in quantum optics for the multi-photon states generated by spontaneous parametric down-conversion [107].…”

Section: Majorana Representationmentioning

confidence: 99%

Classification of Entanglement in Symmetric States

Aulbach

2012

Int. J. Quantum Inform.

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Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis, the entanglement of symmetric multipartite states is categorized, with a particular focus on the pure multi-qubit case and the geometric measure of entanglement. An essential tool for this analysis is the Majorana representation, a generalization of the single-qubit Bloch sphere representation, which allows for a unique representation of symmetric n-qubit states by n points on the surface of a sphere. Here this representation is employed to search for the maximally entangled symmetric states of up to 12 qubits in terms of the geometric measure, and an intuitive visual understanding of the upper bound on the maximal symmetric entanglement is given. Furthermore, it will be seen that the Majorana representation facilitates the characterization of entanglement equivalence classes such as stochastic local operations and classical communication (SLOCC) and the degeneracy configuration (DC). It is found that SLOCC operations between symmetric states can be described by the Möbius transformations of complex analysis, which allows for a clear visualization of the SLOCC freedoms and facilitates the understanding of SLOCC invariants and equivalence classes. In particular, explicit forms of representative states for all symmetric SLOCC classes of up to five qubits are derived. Well-known entanglement classification schemes such as the four qubit entanglement families or polynomial invariants are reviewed in the light of the results gathered here, which leads to sometimes surprising connections. Some interesting links and applications of the Majorana representation to related fields of mathematics and physics are also discussed.

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“…The ground state of 52 Cr is 7 S 3 , constituting the first accessible example of a spin-3 BEC. The spin-3 BEC presents a novel rich ground-state phase diagram at low magnetic fields [12,13,14]. In particular, the existence of biaxial spin-nematic phases [12] opens fascinating links between the spin-3 BECs and the physics of liquid crystals.…”

mentioning

confidence: 99%

Spinor condensates with a laser-induced quadratic Zeeman effect

et al. 2007

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We show that an effective quadratic Zeeman effect can be generated in 52 Cr by proper laser configurations, and in particular by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create S = 1/2 systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems. PACS numbers:Spinor Bose-Einstein condensates (BEC) have recently attracted a growing interest. A spinor gas is formed by atoms in two or more internal states, which can be simultaneously confined by optical dipole traps [1]. Spinor BECs present a rich variety of possible ground states, including ferromagnetic and polar phases for spin-1 BECs [2,3], and an additional cyclic phase for the spin-2 case [4,5]. Elegant topological classifications of the possible spinor ground-states have been recently proposed [6,7]. The spinor dynamics has been also actively studied, in particular the coherent oscillations between the different spinor components [8]. In addition, a spinor gas has been recently quenched across a transition between phases of different symmetries, inducing topological defects [9,10].The recent creation of a Chromium BEC [11] opens new interesting possibilities for the spinor physics. The ground state of 52 Cr is 7 S 3 , constituting the first accessible example of a spin-3 BEC. The spin-3 BEC presents a novel rich ground-state phase diagram at low magnetic fields [12,13,14]. In particular, the existence of biaxial spin-nematic phases [12] opens fascinating links between the spin-3 BECs and the physics of liquid crystals. In addition, 52 Cr has a large magnetic moment µ = 6µ B , where µ B is the Bohr magneton, i.e. six times larger than that of alkali atoms. The corresponding large dipoledipole interaction (DDI) can lead to novel effects in the BEC physics [15]. In particular, dipolar effects were observed for the first time ever in quantum gases in the expansion of a Chromium BEC [16]. The DDI plays also a significant role in the spinor dynamics, since it violates spin conservation, allowing for the transfer of spin into center-of-mass angular momentum, i.e. the equivalent to the Einstein-de Haas effect (EdH) [13,17]. Interestingly, the EdH and other dipolar effects may be also observed in 87 Rb spinor BECs since, in spite of its low µ, the * Present address: TOPTICA Photonics AG, Lochhamer Schlag 19, D-82166 Gräfelfing, Germany.DDI may be significant when compared to the low energy scales associated with the spinor physics [18,19].In the presence of an external magnetic field, B, the different Zeeman sublevels (with quantum number m) of a spinor BEC acquire different shifts due to the linear Zeeman effect (LZE), ∆E LZE (m) = gµ B Bm, with g the Landé factor. The LZE plays no ...

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Inert States of Spin-SSystems

Cited by 53 publications

References 27 publications

Pairing States of Spin- 32 Fermions: Symmetry-Enforced Topological Gap Functions

Pairing States of Spin- 32 Fermions: Symmetry-Enforced Topological Gap Functions

Classification of Entanglement in Symmetric States

Spinor condensates with a laser-induced quadratic Zeeman effect

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