Supersolid states in a spin system: Phase diagram and collective excitations

Abstract

Phases analogous to supersolids can be realized in spin systems. Here we obtain the phase diagram of a frustrated dimer spin-1/2 system on a square lattice and study the collective excitation spectra, focusing on the supersolid state (SS). In the phase diagram on a parameter space of the exchange interaction and magnetic field, we find, on top of the SS phase, a phase that has no counterpart in the Bose Hubbard model and this state becomes dominant at the region where the enhancement of SS occurs in the bose Hubbard model. We then investigate the excitation spectrum and spinspin correlation, which can be detected by neutron scattering experiments. We obtain an analytic expression for the spin wave velocity, which agrees with hydrodynamic relations. The intensity of excitation modes in the spin-spin correlation function is calculated and their change in the supersolid and superfluid states is discussed.PACS numbers: 75.10. Jm, 75.40.Gb, 64.70.Tg, 03.75. Kk INTRODUCTIONSupersolid (SS) state is a phase where both offdiagonal long-range order and diagonal-long range order coexist. After the non-classical rotational inertia experiment in He 4 suggested an SS phase, the SS state attracted considerable interest [1]. However, the interpretation of the result is still controversial [2], and efforts to find SS continue. Lattice systems are other candidates to find SS than He 4 . Cold atoms on optical lattices are one of them. A proposal [3] was made based on the fact that the extended bose Hubbard model with a nearest neighbor interaction shows SS [4,5]. Dipole-dipole interaction is also suggested to help realizing SS [6].Another, entirely different avenue to find SS in lattice systems is to consider quantum magnets. This is because certain spin systems can be effectively regarded as bose systems [7][8][9]. After a theoretical proposal of SS in a dimer spin system [10], spin systems are attracting much attention as a promising candidate to find SS phases [10][11][12][13][14][15]. One example is the spin-1 Heisenberg model with an anisotropy, which is effectively obtained from a spin-1 frustrated dimer model [11]. Another example is the spin-1/2 dimer model with large Ising-like exchange anisotropy [10,12]. The anisotropy can be effectively realized in a lattice with large frustration. Ref. [13] has investigated a frustrated spin-1/2 spin-dimer Heisenberg model with spin-isotropic couplings on square lattice( Fig.1), and shown that the model actually exhibits a SS state. However, the study was concentrated on a specific choice of parameters, while the phase diagram in a wider parameter space has yet to be determined. In addition, experimentally relevant properties of the SS phase have not been fully understood, either.These have motivated us, in the present work, to investigate the phase diagram and dynamical properties of the frustrated spin-1/2 dimer Heisenberg model on square lattice. There, we employ the bond operator method as well as the generalized spin wave theory. In the phase diagram on a parameter space of t...

Stripe phases in a frustrated spin-1/2 dimer Heisenberg model

“…The intermediate regions where stripe superfluidity and stripe TS order coexist would exhibit a S-SS phase. In addition, we also found a striped "superfluid" (S-"SF") as a counterpart of "superfluid" ("SF") that has been found by Murakami et al 12 Then we investigate the excitation spectrum obtained by spin-wave theory and show their behavior in different phases and boundaries. We found spin-wave velocity is anisotropic in the S-SF and S-SS phases, which could be detected experimentally.…”

“…8,9 For the system without anisotropy, but with frustration, recent works based on various reliable methods also reveal the existence of SS. [10][11][12] In this work, we investigate the effect of frustrations more extended. We introduce frustrations in both cardinal and corner directions to see whether more interesting phases can be found.…”

Сверхтвердая Магнитная Фаза В Двумерном Изингоподобном Антиферромагнетике С Большой Одноионной Анизотропией

“…Кроме того, как было доказано в [26,27], приближение среднего поля можно использовать при рассмотрении систем лю-бой размерности. Также необходимо отметить работу [5], где было показано, что приближение среднего поля дает правильные результаты для модели Гейзенберга с фрустрированным обменным взаимодействием для спина 1/2, в частности при исследовании сверхтвердой магнитной фазы. Решая уравнение Шредингера с гамильтонианом (3), найдем уровни энергии магнитного иона и его собствен-ные функции…”

“…Помимо газов в оптических решетках сверхтвердую магнитную фазу можно обнаружить и в других кван-товых магнетиках [5][6][7][8][9][10]. После того как была до-казана возможность реализации сверхтвердой фазы в двухподрешеточных спиновых системах [11,12], такие системы стали одними из перспективных кандидатов для обнаружения данного состояния [11,[13][14][15][16][17][18][19].…”

High-order study of the quantum critical behavior of a frustrated spin- 12 antiferromagnet on a stacked honeycomb bilayer

“…Such field-induced spin supersolidity has particularly been investigated for various frustrated spin-1 2 models on a square-lattice bilayer [8,[22][23][24][25][26][27].…”