Using an exact-diagonalization technique on small clusters, we calculate the spin and density excitation spectra as well as the temperature dependence of the specific heat for the triangular-lattice t-J model with the multiple-spin exchange interactions, whereby we consider the low-energy excitations of the two-dimensional liquid 3He adsorbed on graphite. We find that, for a relevant set of the parameter values, the spectral weight for the spin excitations is concentrated on a very low-energy region, while that of the density excitations extends over a wide energy range, indicating the clear separation of their energy scales. The double-peak structure in the temperature dependence of the specific heat is also obtained. © 2009 IOP Publishing Ltd.Ministry of Education, Culture, Sports, Science and Technology of Japan/18028008Ministry of Education, Culture, Sports, Science and Technology of Japan/18043006Ministry of Education, Culture, Sports, Science and Technology of Japan/18540338Ministry of Education, Culture, Sports, Science and Technology of Japan/19014004JSPS Research Fellowship for Young Scientist

Ohta, Y.

Seki, K.

Shirakawa, T.

Journal of Physics : Conference Series

Institutionelles Repositorium der Leibniz Universität Hannover

This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 194.95.157.184This content was downloaded on 05/05/2017 at 08:41Please note that terms and conditions apply.Spin and mass excitations in the doped multiple spin exchange model on a triangular lattice:3He on graphiteView the table of contents for this issue, or go to the journal homepage for more2009 J. Phys.: Conf. Ser. 150 032095(http://iopscience.iop.org/1742-6596/150/3/032095)Home Search Collections Journals About Contact us My IOPscienceYou may also be interested in:Combination of ferromagnetic and antiferromagnetic features in Heisenberg ferrimagnetsShoji Yamamoto, Takahiro Fukui, Klaus Maisinger et al.Specific heat of the spin-\half Heisenberg antiferromagnet on squagome latticePiotr Tomczak and Johannes RichterSeveral- and Many-Electron Artificial-Atoms at Filling Factors between 2 and 1Guy Austing, Yasuhiro Tokura, Takashi Honda et al.‘Spin-disentangled’ exact diagonalization of repulsive Hubbard systemsMichele Cini, Gianluca Stefanucci, Enrico Perfetto et al.Spin and Mass Excitations in the Doped MultipleSpin Exchange Model on a Triangular Lattice:3He on GraphiteK Seki1, T Shirakawa1;2 and Y Ohta11Department of Physics, Chiba University, Chiba 263-8522, Japan2Institut fur Theoretische Physik, Leibniz Universitat Hannover, D-30167 Hannover, GermanyAbstract. Using an exact-diagonalization technique on small clusters, we calculate the spinand density excitation spectra as well as the temperature dependence of the specic heat for thetriangular-lattice t-J model with the multiple-spin exchange interactions, whereby we considerthe low-energy excitations of the two-dimensional liquid 3He adsorbed on graphite. We ndthat, for a relevant set of the parameter values, the spectral weight for the spin excitations isconcentrated on a very low-energy region, while that of the density excitations extends overa wide energy range, indicating the clear separation of their energy scales. The double-peakstructure in the temperature dependence of the specic heat is also obtained.1. Introduction3He atoms adsorbed on a graphite surface is known to be an ideal two-dimensional correlatedfermion system. A variety of phenomena have been found to appear depending on the densityof 3He atoms in the second layer, including a correlated fermi-liquid phase and a solidiedcommensurate phase at a 4=7 density of the underlying rst layer [1, 2]. The latter 4=7phase has been studied by using the triangular-lattice Heisenberg model with the multiple-spin exchange interactions [3, 4], where the opening of the spin gap has been suggested [5].However, experiments on the magnetic susceptibility [4, 6] and specic heat [7, 8] indicate thatthe system has the gapless nature of the quantum spin liquid. A double-peak structure in thetemperature dependence of the specic heat has also been reported in the doped-Mott region ofmonolayer 3He [9].Recently, Watanabe and Imada [10] pointed out that the density uctuations between thesecond and third layers of 3He atoms are essential for understanding the gapless spin-liquidnature. Then, Fuseya and Ogata [11] proposed the doped triangular-lattice t-J model withmultiple-spin exchange interactions as an eective model for the doped-Mott region of this systemand obtained the ground-state phase diagram of the model. The low-energy excitations of themodel were also discussed. They thereby argued that there is an anomalous quantum-liquidphase, characteristic of the spin-charge separation, which may be relevant with the anomalousfeatures observed in the 3He system.Motivated by such developments in the eld, we study in this paper the triangular-latticet-J model with the multiple-spin exchange interactions further. In particular, we directlycalculate the spin and density excitation spectra and single-particle spectra as well as thetemperature dependence of the specic heat and uniform magnetic susceptibility by using the25th International Conference on Low Temperature Physics (LT25) IOP PublishingJournal of Physics: Conference Series 150 (2009) 032095 doi:10.1088/1742-6596/150/3/032095c© 2009 IOP Publishing Ltd 1exact-diagonalization technique on small clusters. We thus discuss the peculiar nature of thelow-energy physics of the system.2. Model and methodThe triangular-lattice t-J model with the multiple-spin exchange interactions is dened by theHamiltonianH =  tXhiji;h(1  ni; )cyicj(1  nj; ) + H:c:i+ JXhijiSi  Sj   ninj4+ KXhijkli(P4 + P 14 ) + SXhijklmni(P6 + P 16 ) (1)where ci is the annihilation operator of a fermion (3He atom) at site i and spin  (="; #)),Si is the spin-1/2 operator, and ni (= ni" + ni#) is the number operator. P4 and P6 are thefour-spin and six-spin operators, respectively. The nearest-neighbor hopping parameter t andtwo-spin and four-spin exchange interaction parameters J and K are estimated as follows [11]:t = 50  100 mK,  J = 1  10 mK, and K=jJ j  0:2. S is small and is neglected in this paper.Throughout the paper, we use t = 1 as the unit of energy and we set h = kB = 1.We use the Lanczos exact-diagonalization technique on small clusters to calculate the groundstate and excitation spectra of the model. In particular, we study the dynamical spin ( = s)and density ( = d) correlation functions dened asC(q; !) =1=h	0jOy1!   (H E0)  iOj	0i (2)where 	0 and E0 are the ground-state wave function and energy, respectively, and O is theFourier transform of either the spin (12(ni"   ni#)) or density (ni" + ni#) operator. We deneS(q; !) (= Cs(q; !)) and N(q; !) (= Cd(q; !)). We also calculate the single-particle spectralfunction A(k; !) to see the dynamics of a doped hole and possible quasiparticle dispersionand fermi-surface topology. We use a cluster of 20 sites with periodic boundary condition forthese calculations. To calculate the temperature dependence of the specic heat C(T ) anduniform magnetic susceptibility (T ), the Hamiltonian for a smaller-size cluster of 12 sites isfully diagonalized.3. Results of calculationBefore discussing our results, let us rst briey review the ground-state phase diagram obtainedby Fuseya and Ogata [11]. Phases obtained are as follows: the region of phase separation(phase-I), the region of fermi liquid with strong spin uctuations (phase-II), the region of new-type quantum liquid (phase-III), and the region of ferromagnetism (phase-IV). They put specialemphasis on the phase-III, which is argued to be the region of spin-charge separation and maybe relevant with the anomalous features of the 3He system. In the following, we in particularexamine the region of phase-III using the parameter values J =  0:3 and K = 0:06, which wecompare with the results of other regions, i.e., the phases II (J =  0:3 and K = 0:15  0:2) andIV (J =  0:3 and K = 0).Now let us discuss our results. First, we discuss the spin and density excitation spectracalculated for the region of phase-III. The results are shown in Fig. 1. We nd the following:The spectral weight for the spin excitations is concentrated on a very low-energy region of about! < 0:8t. This reects the presence of a large number of nearly degenerate low-energy statescoming from the frustrated nature of the spin degrees of freedom. The low-energy spectralweight is extended over the entire Brillouin zone, reecting the spatially localized nature of spin25th International Conference on Low Temperature Physics (LT25) IOP PublishingJournal of Physics: Conference Series 150 (2009) 032095 doi:10.1088/1742-6596/150/3/0320952ωωωωωωq1q2q3q4q5q6q0q1q2q3q4q5q6Figure 1. Calculated spin and density excitation spectra of the t-J-K model at J =  0:3and K = 0:06. We use the 20-site cluster with two holes (10% doping). The spectra for thenoninteracting innite system N0(q; !) are also shown for comparison. Inset: Brillouin zone andmomenta at which the spectra are calculated.uctuations. The spectral weight for the density excitations, on the other hand, extends overthe wide energy range of about 0 < ! < 9t (entire band width), which is more or less resemblesthe spectrum of the noninteracting system. From these results, we may say that the spin anddensity excitations are clearly separated in their energy scales. With increasing K, we nd theupward shift of the low-energy spectral weight of the spin excitations; e.g., at K = 0:2, we ndthe peaks at a higher-energy region of about 0 < ! < 2t, where the momentum dependence ofthe positions of the peaks becomes signicant as well. Thus, the separation between the energyscales of the spin and density excitations becomes weaker.0.0 0.2 0.4 0.6 0.8 1.0012345 K = 0.15K = 0  C(T)TK = 0.06Figure 2. Calculated temperature dependence of the specic heat of the t-J-K model atJ =  0:3. We use a cluster of 12 sites with two holes.Temperature dependence of the specic heat C(T ) calculated for the 12-site clusters with two25th International Conference on Low Temperature Physics (LT25) IOP PublishingJournal of Physics: Conference Series 150 (2009) 032095 doi:10.1088/1742-6596/150/3/0320953holes is shown in Fig. 2. We nd that there appears the double-peak structure in C(T ) when weuse the parameter set corresponding to the anomalous quantum-liquid phase (phase-III); i.e., asharp peak at low temperature that comes from the spin excitations and a broad peak extendingover high temperatures that comes from the density excitations. In fact, the temperature rangescorrespond well to the energies of the spectral weight of the spin and density excitations (seeFig. 1). The obtained two-peak structure is consistent with experiment [8, 9]. We also nd thatthe uniform magnetic susceptibility calculated shows unique temperature variations, dependingon the value of K.We also calculate the single-particle spectral function A(k; !) both at half lling to examinethe propagation of a single hole and at a two-hole doping level to examine the possiblequasiparticle dispersion and fermi-surface topology. The results will be presented elsewhere [12]but we nd the following: The sharp quasiparticle-like peaks with a characteristic dispersionappear at the lowest energies in the spectra at half lling, just as in the square-lattice t-Jmodel; this is in particular the case at K = 0:2 but remains signicant even at K = 0:06.Further analyses are required to clarify the nature of the hole dynamics, quasiparticle dispersionand fermi-surface topology in this system, which will be presented elsewhere [12].4. SummaryTo consider the low-energy excitations of the two-dimensional liquid 3He adsorbed on graphite,we have calculate the spin and density excitation spectra as well as the temperature dependenceof the specic heat for the triangular-lattice t-J model with the multiple-spin exchangeinteractions by an exact-diagonalization technique on small clusters. We have shown fora relevant set of the parameter values that the spectral weight for the spin excitations isconcentrated on a very low-energy region, while that of the density excitations extends overa wide energy range. We have also shown that the double-peak structure appears in thetemperature dependence of the specic heat, with the identication that the low-temperaturepeak corresponds to the spin excitations and the high-temperature broad peak corresponds tothe density excitations. We have thus demonstrated that the spin and density excitations areclearly separated in their energy scales. Further details will be published elsewhere [12].AcknowledgmentsThis work was supported in part by Grants-in-Aid for Scientic Research (Nos. 18028008,18043006, 18540338, and 19014004) from the Ministry of Education, Culture, Sports, Scienceand Technology of Japan. TS acknowledges nancial support from JSPS Research Fellowshipfor Young Scientists. A part of computations was carried out at the Research Center forComputational Science, Okazaki Research Facilities, and the Institute for Solid State Physics,University of Tokyo.References[1] Elser V 1989 Phys. Rev. Lett. 62 2405[2] Greywall D S 1990 Phys. Rev. B 41 1842[3] Roger M, Bauerle C, Munkov Y M, Chen A S and Godfrin H 1998 Phys. Rev. Lett. 80 1308[4] Ikegami H, Masutomi R, Obara K and Ishimoto H 2000 Phys. Rev. Lett. 85 5146[5] Misguich G, Bernu B, Lhuillier C and Waldmann C 1998 Phys. Rev. Lett. 81 1098[6] Masutomi R, Karaki Y and Ishimoto H 2004 Phys. Rev. Lett. 92 025301[7] Ishida K, Morishita M, Yawata K and Fukuyama H 1997 Phys. Rev. Lett. 79 3451[8] Matsumoto Y, Tsuji D, Murakawa S, Akisato H, Kambara H and Fukuyama H 2005 J. Low Temp. Phys.138 271[9] Matsumoto Y, Tsuji D, Murakawa S, Bauerle C, Kambara H and Fukuyama H 2007 unpublished[10] Watanabe S and Imada M 2007 J. Phys. Soc. Jpn. 76 113603[11] Fuseya Y and Ogata M 2008 J. Phys. Soc. Jpn. preprint cond-mat/0804.4329[12] Seki K, Shirakawa T and Ohta Y 2008 in preparation.25th International Conference on Low Temperature Physics (LT25) IOP PublishingJournal of Physics: Conference Series 150 (2009) 032095 doi:10.1088/1742-6596/150/3/0320954

Spin and mass excitations in the doped multiple spin exchange model on a triangular lattice: 3He on graphite

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