Bose-Einstein Condensation in Quantum Magnets

C. Kollath; T. Giamarchi; C. Rüegg

doi:10.1017/9781316084366.030

28 - Bose-Einstein Condensation in Quantum Magnets

from Part IV - Condensates in Condensed Matter Physics

Published online by Cambridge University Press: 18 May 2017

C. Kollath ,

T. Giamarchi and

Edited by

David W. Snoke and

C. Kollath: Affiliation:
HISKP, University of Bonn
T. Giamarchi: Affiliation:
University of Geneva, Geneva
C. Rüegg: Affiliation:
University of Geneva, Department of Quantum Matter Physics, Switzerland
Nick P. Proukakis: Affiliation:
Newcastle University
David W. Snoke: Affiliation:
University of Pittsburgh
Peter B. Littlewood: Affiliation:
University of Chicago

Book contents

Get access

Summary

The recent experimental advances in the field of quantum spin materials have led to well-controlled systems which can be used in order to simulate complex quantum models in a clean fashion. Here we discuss how fascinating effects normally known from bosonic systems such as the Bose-Einstein condensation can be investigated with the help of such materials. We discuss as an example how a crossover between an effectively one-dimensional geometry described by a Luttinger liquid to a three-dimensional Bose-Einstein condensation can be induced. Additionally, we point out how more complex phases as the Bose-glass phase could be realized in these quantum magnets.

Introduction

Although it can seem paradoxical, the quantum magnetic states found in insulators offer an interesting route to study Bose-Einstein condensation (BEC) and more generally phenomena related to itinerant, interacting bosonic systems.

In many materials, the repulsion between the electrons causes the ground state to be a Mott insulator with one electron localized per site. In such a case, the charge degrees of freedom are completely locked by large charge gaps (usually of the order of tens of electron volts). However, one can study the fascinating physics of the spin degrees of freedom. As was shown a long time ago, the localized spins are coupled by a so-called superexchange which may be ferro- or antiferromagnetic. The properties of the exchange coupling between the spins depend mainly on the underlying atomic structure of the material. The resulting physics is extremely rich and such materials can have a host of phases ranging from ordered magnetic phases to so-called spin-liquid phases in which spin–spin correlations decay extremely fast with distance. The field of research concerning these materials, dubbed quantum magnetism, is thus an extremely active field in its own right [1].

Additionally, one can exploit the formal mapping that exists between spin operators and bosonic ones, as will be described in the next section, to connect the magnetic materials to itinerant bosonic systems with interactions between the bosons. This opens the way to use such quantum spin systems as quantum simulators. A quantum simulator means that the experimental system can be employed in order to “solve” in a controlled way a problem/Hamiltonian known from a different less controlled physical realization, e.g., inspired by fundamental many-body physics, quantum information or computational applications.

Type: Chapter
Information: Universal Themes of Bose-Einstein Condensation , pp. 549 - 568

DOI: https://doi.org/10.1017/9781316084366.030 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Auerbach, A. 1998. Interacting Electrons and Quantum Magnetism. Berlin: Springer.

[2] Holstein, T., and Primakoff, H. 1940. Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev., 58, 1098.Google Scholar

[3] Matsubara, T., and Matsuda, H. 1956. A lattice model of liquid helium. Prog. Theor. Phys., 16, 569.Google Scholar

[4] Giamarchi, T., and Tsvelik, A. M. 1999. Coupled ladders in a magnetic field. Phys. Rev. B, 59, 11398.Google Scholar

[5] Giamarchi, T., Rüegg, Ch., and Tchernyshyov, O. 2008. Bose-Einstein condensation in magnetic insulators. Nature Physics, 4, 198.Google Scholar

[6] Zapf, V., Marcelo, J., and Batista, C. D. 2014. Bose-Einstein condensation in quantum magnets. Rev. Mod. Phys., 86, 563.Google Scholar

[7] Affleck, I. 1991. Bose condensation in quasi-one-dimensional antiferromagnets in strong fields. Phys. Rev. B, 43, 3215.Google Scholar

[8] Chitra, R., and Giamarchi, T. 1997. Critical properties of gapped spin-chains and ladders in a magnetic field. Phys. Rev. B, 55, 5816.Google Scholar

[9] Pitaevskii, L., and Stringari, S. 2003. Bose-Einstein Condensation. Oxford: Clarendon Press.

[10] Pethick, C. J., and Smith, H. 2002. Bose-Einstein Condensation in Dilute Gases. Cambridge: Cambridge University Press.

[11] Popov, V. N. 1987. Functional Integrals and Collective Excitations. Cambridge: Cambridge University Press.

[12] Sachdev, S., and Bhatt, R. N. 1990. Bond-operator representation of quantum spins: mean-field theory of frustrated quantum Heisenberg antiferromagnets. Phys. Rev. B, 41, 9323.Google Scholar

[13] Normand, B., and Rüegg, Ch. 2011. Complete bond-operator theory of the two-chain spin ladder. Phys. Rev. B, 83, 054415.Google Scholar

[14] Gogolin, A. O., Nersesyan, A. A., and Tsvelik, A. M. 1999. Bosonization and Strongly Correlated Systems. Cambridge: Cambridge University Press.

[15] Giamarchi, T. 2004. Quantum Physics in One Dimension. Vol. 121. Oxford: Oxford University Press.

[16] Cazallila, M. A., Citro, R., Giamarchi, T., Orignac, E., and Rigol, M. 2011. One dimensional bosons: from condensed matter systems to ultracold gases. Rev. Mod. Phys., 83, 1405.Google Scholar

[17] Caux, J.-S., Calabrese, P., and Slavnov, N. A. 2007. One-particle dynamical correlations in the one-dimensional Bose gas. J. Stat. Mech.: Theor. Exp., 2007, P01008.Google Scholar

[18] Pollet, L. 2012. Recent developments in quantum Monte Carlo simulations with applications for cold gases. Reports on Progress in Physics, 75, 094501.Google Scholar

[19] Schollwöck, U. 2011. The density-matrix renormalization group in the age of matrix product states. Annals of Physics, 326, 96.Google Scholar

[20] Nikuni, T., Oshikawa, M., Oosawa, A., and Tanaka, H. 2000. Bose-Einstein condensation of dilute magnons in TlCuCl3. Phys. Rev. Lett., 84, 5868.Google Scholar

[21] Cavadini, N., Heigold, G., Henggeler, W., Furrer, A., Güdel, H.-U., Krämer, K., and Mutka, H. 2001. Magnetic excitations in the quantum spin system TlCuCl3. Phys. Rev. B, 63, 172414.Google Scholar

[22] Sirker, J., Weisse, A., and Sushkov, O. P. 2004. Consequences of spin-orbit coupling for the Bose-Einstein condensation of magnons. Europhys. Lett., 68, 275.Google Scholar

[23] Yamada, F., Ono, T., Tanaka, H., Misguich, G., Oshikawa, M., and Sakakibara, T. 2008. Magnetic-field induced Bose-Einstein condensation of magnons and critical behavior in interacting spin dimer system TlCuCl3. Journal of the Physical Society of Japan, 77, 013701.Google Scholar

[24] Batyev, E. G., and Braginskii, L. S. 1984. Antiferrornagnet in a strong magnetic field: analogy with Bose gas. Journal of Experimental and Theoretical Physics, 60, 781.Google Scholar

[25] Oosawa, A., Katori, H. Aruga, and Tanaka, H. 2001. Specific heat study of the fieldinduced magnetic ordering in the spin-gap system TlCuCl3. Phys. Rev. B, 63, 134416.Google Scholar

[26] Tanaka, H., Oosawa, A., Kato, T., Uekusa, H., Ohashi, Y., Kakurai, K., and Hoser, A. 2001. Observation of field-induced transverse neel ordering in the spin gap system TlCuCl3. Journal of the Physical Society of Japan, 70, 939.Google Scholar

[27] Rüegg, Ch., Cavadini, N., Furrer, A., Güdel, H.-U., Krämer, K., Mutka, H., Habicht, A. K., and Vorderwisch, P. 2003. Bose-Einstein condensation of the triplet states in the magnetic insulator TlCuCl3. Nature, 423, 62.Google Scholar

[28] Giamarchi, T. 2012. Some experimental tests of Tomonaga-Luttinger liquids. Int. J. Mod. Phys. B, 26, 1244004.Google Scholar

[29] Klanjšek, M., Mayaffre, H., Berthier, C., Horvatić, M., Chiari, B., Piovesana, O., Bouillot, P., Kollath, C., Orignac, E., Citro, R., and Giamarchi, T. 2008. Controlling Luttinger liquid physics in spin ladders under a magnetic field. Phys. Rev. Lett., 101, 137207.Google Scholar

[30] Thielemann, B., Rüegg, Ch., Rønnow, H. M., Läuchli, A. M., Caux, J.-S., Normand, B., Biner, D., Krämer, K. W., Güdel, H.-U., Stahn, J., Habicht, K., Kiefer, K., Boehm, M., McMorrow, D. F., and J., Mesot. 2009a. Direct observation of magnon fractionalization in the quantum spin ladder. Phys. Rev. Lett., 102, 107204.Google Scholar

[31] Thielemann, B., Rüegg, Ch., Kiefer, K., Rønnow, H. M., Normand, B., Bouillot, P., Kollath, C., Orignac, E., Citro, R., Giamarchi, T., Läuchli, A. M., Biner, D., Krämer, K. W., Wolff-Fabris, F., Zapf, V. S., Jaime, M., Stahn, J., Christensen, N. B., Grenier, B., McMorrow, D. F., and Mesot, J. 2009b. Field-controlled magnetic order in the quantum spin-ladder system (Hpip)2CuBr4. Phys. Rev. B, 79, 020408(R).Google Scholar

[32] Bouillot, P., Kollath, C., Läuchli, A. M., Zvonarev, M., Thielemann, B., Rüegg, Ch., Orignac, E., Citro, R., Horvatić, M., Berthier, C., Klanjšek, M., and Giamarchi, T. 2011. Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field. Phys. Rev. B, 83, 054407.Google Scholar

[33] Schmidiger, D., Bouillot, P., Guidi, T., Bewley, R., Kollath, C., Giamarchi, T., and Zheludev, A. 2013. Spectrum of a magnetized strong-leg quantum spin ladder. Phys. Rev. Lett., 111, 107202.Google Scholar

[34] Povarov, K. Yu., Schmidiger, D., Reynolds, N., Bewley, R., and Zheludev, A. 2015. Scaling of temporal correlations in an attractive Tomonaga-Luttinger spin liquid. Phys. Rev. B, 91, 020406.Google Scholar

[35] Giamarchi, T. 2010. Quantum phase transitions in quasi-one dimensional systems. Page 291 of: Carr, Lincoln D. (ed), Understanding Quantum Phase Transitions. CRC Press / Taylor & Francis.

[36] Rüegg, Ch., Kiefer, K., Thielemann, B., McMorrow, D. F., Zapf, V., Normand, B., Zvonarev, M. B., Bouillot, P., Kollath, C., Giamarchi, T., Capponi, S., Poilblanc, D., Biner, D., and Krämer, K. W. 2008. Thermodynamics of the spin Luttinger liquid in a model ladder material. Phys. Rev. Lett., 101, 247202.Google Scholar

[37] Giamarchi, T., and Schulz, H. J. 1988. Anderson localization and interactions in onedimensional metals. Phys. Rev. B, 37, 325.Google Scholar

[38] Fisher, M. P. A., Weichman, P. B., Grinstein, G., and Fisher, D. S. 1989. Boson localization and the superfluid-insulator transition. Phys. Rev. B, 40, 546.Google Scholar

[39] Hong, T., Zheludev, A., Manaka, H., and Regnault, L.-P. 2010. Evidence of a magnetic Bose glass in (CH3)2CHNH3Cu(Cl0.95Br0.05)3 from neutron diffraction. Phys. Rev. B, 81, 060410.

[40] Yamada, F., Tanaka, H., Ono, T., and Nojiri, H. 2011. Transition from Bose Gass to a condensate of triplons in Tl1-xKxCuCl3. Phys. Rev. B, 83, 020409.Google Scholar

[41] Yu, R., Yin, L., Sullivan, N. S., Xia, J. S., Huan, C., Paduan-Filho, A., Oliveira, N. F.Jr., Haas, S., Steppke, A., Miclea, C. F., Weickert, F., Movshovich, R., Mun, E.-D., Scott, B. S., Zapf, V. S., and Roscilde, T. 2012. Bose glass and Mott glass of quasiparticles in a doped quantum magnet. Nature, 489, 379.Google Scholar

[42] Ward, S., Bouillot, P., Ryll, H., Kiefer, K., Kramer, K. W., Ruegg, C., Kollath, C., and Giamarchi, T. 2013. Spin ladders and quantum simulators for Tomonaga-Luttinger liquids. J. Phys.: Condens. Matter, 25, 014004.Google Scholar

Book contents

28 - Bose-Einstein Condensation in Quantum Magnets

Summary

Access options

References

Save book to Kindle

Save book to Dropbox

Save book to Google Drive