Low-temperature properties of the random Heisenberg antiferromagnetic chain

Dasgupta, Chandan; Ma, Shang‐keng

doi:10.1103/physrevb.22.1305

Cited by 506 publications

(510 citation statements)

References 11 publications

Supporting

Mentioning

494

Contrasting

Unclassified

Order By: Relevance

“…Meanwhile, it was recently suggested in ref. [33] that the QSL of the triangular-lattice organic salts might be the randomness-induced one, the randomsinglet [34][35][36] or the valence-bond glass (VBG) state [37,38], in which the randomness is self-generated for the spin degrees of freedom at low temperatures via the random freezing of the electric-polarization degrees of freedom [6,10]. Such a randomness-induced QSL picture apparently explains many of the experimentally observed features of the triangular organic salts [33].…”

mentioning

confidence: 99%

Quantum Spin-Liquid Behavior in the Spin-1/2 Random-Bond Heisenberg Antiferromagnet on the Kagome Lattice

2014

View full text Add to dashboard Cite

The effect of the quenched bond-randomness on the ordering of the S = 1/2 antiferromagnetic Heisenberg model on the kagome lattice is investigated by means of an exact-diagonalization method. When the randomness exceeds a critical value, the ground state of the model exhibits a transition within the non-magnetic state into the randomness-relevant gapless spin-liquid state. Implications to the S = 1/2 kagome-lattice antiferromagnet herbertsmithite is discussed.Since the proposal by P.W. Anderson of the resonating valence bond state [1], the quantum spin-liquid (QSL) state possibly realized in certain S = 1/2 frustrated magnets has attracted interest of researchers [2]. After a long experimental quest, several candidate materials were recently reported in geometrically frustrated magnets, including both the triangular-lattice and the kagome-lattice antiferromagnets (AFs).Examples of the triangular-lattice AF might be S = 1/2 organic salts such as κ-(ET) 2 Cu 2 (CN) 3 [3][4][5][6] and [7][8][9][10], which exhibit no magnetic ordering, neither regular nor random, down to a very low temperature. The QSL state of these compounds exhibits gapless behaviors characterized by, e.g., the lowtemperature specific heat [4,9] or the thermal conductivity [5,8] linear in the absolute temperature T . An example of the second category, the kagome-lattice AF, might be herbertsmithite CuZn 3 (OH) 6 Cl 2 [11][12][13][14][15][16][17]. No magnetic order is observed down to 20mK in spite of the exchange coupling of 180K, while gapless behaviors are observed in various physical quantities.The origin of the QSL behavior observed in these triangular-lattice organic salts and the kagome-lattice herbertsmithite has attracted tremendous interest, and various theoretical proposals have been made. The simplest possible reference model might be the S = 1/2 AF Heisenberg model with the nearest-neighbor (n.n.) bilinear coupling. In the triangular case, the ground state of such n.n. model is known to be the standard AF longrange order (LRO), the 120-degrees structure [18,19]. Hence, to explain the QSL behavior observed in these organic salts, some ingredient not taken into account in the simplest Heisenberg model is required. In the kagome case, by contrast, the ground state of the n.n. model is believed to be some sort of QSL state without the magnetic LRO, although its nature is still under hot debate. Various scenarios, including the Z 2 spin liquid [20][21][22][23][24], the algebraic U(1) spin liquid [25][26][27][28], the chiral spin liquid [29] and the valence bond crystal (VBC) [30][31][32] etc. have been proposed. It is not entirely clear at the present stage, however, which of these, or any of these, applies to the experimentally observed QSL state of herbertsmithite.Most of the recent theories pre-assumes that the system is clean enough that the quenched randomness plays a negligible role. Meanwhile, it was recently suggested in ref. [33] that the QSL of the triangular-lattice organic salts might be the randomness-induced one, the randomsi...

show abstract

mentioning

confidence: 99%

Quantum Spin-Liquid Behavior in the Spin-1/2 Random-Bond Heisenberg Antiferromagnet on the Kagome Lattice

2014

View full text Add to dashboard Cite

show abstract

“…It seems to be established right now that the critical properties in these one-dimensional system are governed by an infinite-disorder fixed-point [9] and the application of a renormalization group (RG) schemeá la Dasgupta and Ma [10] is a powerful tool to determine critical properties and static correlations of these new universality classes, either analytically, if possible, or numerically. Although the underlying renormalization scheme is extremely simple the analytical computations are sometimes tedious [1,2].…”

mentioning

confidence: 99%

Absence of dynamical crossover in the vortex creep near by the second peak effect in superconducting Hg-1201 single crystals

Daignere¹,

Aouaroun²,

Simon³

2000

Eur. Phys. J. B

View full text Add to dashboard Cite

We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their quantum phase transition driven by the anisotropy and dimerization, respectively. Using exact expressions for magnetization, correlation functions and energy gap, obtained by the free fermion technique, the critical and off-critical (Griffiths-McCoy) singularities are related to persistence properties of random walks. In this way we determine exactly the decay exponents for surface and bulk transverse and longitudinal correlations, correlation length exponent and dynamical exponent.Disordered quantum spin chains have gained much interest recently [1][2][3][4][5][6][7][8]. It seems to be established right now that the critical properties in these one-dimensional system are governed by an infinite-disorder fixed-point [9] and the application of a renormalization group (RG) schemeá la Dasgupta and Ma [10] is a powerful tool to determine critical properties and static correlations of these new universality classes, either analytically, if possible, or numerically. Although the underlying renormalization scheme is extremely simple the analytical computations are sometimes tedious [1,2]. Therefore an alternative route to the exact determination of critical exponents and other quantities of interest is highly desirable, and this is what we are going to present in this letter. In doing so we follow a route on which we already traveled successfully for the random transverse Ising chain [11][12][13], and here we are going to do one step further studying random XX and XY models with the help of a straightforward and efficient mapping to random walk problems. This mapping is not only a short-cut to the results known from analytical RG calculations, it also gives new exact results in the off-critical region (the Griffiths-phase [14]) and provides a mean to study situations in which the RG procedure must fail, as for instance in the case of correlated disorder [15]. Here we confine ourselves to a concise presentation of the basic ideas including the determination of various exponents for the first time. The technical details of the derivations and further results are deferred to a subsequent publication [16].The model that we consider is a spin-1/2 XY-quantum spin chain with L sites and open boundaries, defined by the Hamiltonianwhere the S x,y l are spin-1/2 operators and the interaction strengths or couplings J x,y l > 0 are independent random variables modeling quenched disorder. In the case of the random XY chain one has two independent distributions for the couplings J x and J y , ρ x and ρ y , respectively, whereas the random dimerized XX-chain has perfectly isotropic couplings J x l = J y l = J l but two independent probability distributions for the even and odd couplings (i.e. for J 2l = J e 2l and J 2l−1 = J o 2l−1 ), ρ e and ρ o , respectively.The model (1) where var(x) is the variance of random variable x. At the critical point (δ = 0) spatial correlations decay algebraically, for instance in a finite system of length L with periodic bounda...

show abstract

“…The staggered magnetization at site i is m i = ͑−1͒ i ͗S i ͘. The resulting effective 1D problem can be solved using the RSRG method, 3,4 from which the phase diagrams of the systems have been obtained for various cases. 36 In the present work we go beyond the static mean-field approximation and calculate the dynamical response functions by treating interchain couplings within the RPA, from which we also obtain the collective mode spectrum of the system.…”

mentioning

confidence: 99%

“…We go beyond mean-field theory by allowing the Néel order parameter to fluctuate, and treat the interchain coupling using the random-phase approximation ͑RPA͒, while tackling the intrachain coupling using the real-space renormalization-group ͑RSRG͒ method. 3,4 The RSRG technique has been proven to be powerful in obtaining magnetic and thermodynamics properties of random spin chains. Various numerical techniques [21][22][23] have also been deployed to study random chains and their results agree with those obtained by RSRG.…”

mentioning

confidence: 99%

“…1 The one-dimensional nature of such systems allowed for tremendous theoretical progress both in clean systems by using exact solution and field theory mapping 1,2 and disordered systems within renormalization-group framework. [3][4][5][6][7][8] While such one-dimensional models have remarkably rich physics, in general, they do not give a complete description of real systems. Real spin chain compounds, such as CuGeO 3 ͑Ref.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of weakly coupled random antiferromagnetic quantum spin chains

Yusuf

Yang

2005

Phys. Rev. B

View full text Add to dashboard Cite

We study the low-energy collective excitations and dynamical response functions of weakly coupled random antiferromagnetic spin-1 / 2 chains. The interchain coupling leads to Néel order at low temperatures. We use the real-space renormalization-group technique to tackle the intrachain couplings and treat the interchain couplings within the random phase approximation ͑RPA͒. We show that the system supports collective spin wave excitations, and calculate the spin wave velocity and spectra weight within RPA. Comparisons will be made with inelastic neutron scattering experiments on quasi-one-dimensional disordered spin systems such as doped CuGeO 3 . DOI: 10.1103/PhysRevB.72.020403 PACS number͑s͒: 75.10.Jm, 75.30.Cr, 75.30.Ds, 75.50.Ee Antiferromagnetic ͑AF͒ quantum spin chains have been of interest to physicists since the early days of quantum mechanics. 1 The one-dimensional nature of such systems allowed for tremendous theoretical progress both in clean systems by using exact solution and field theory mapping 1,2 and disordered systems within renormalization-group framework. 3-8 While such one-dimensional models have remarkably rich physics, in general, they do not give a complete description of real systems. Real spin chain compounds, such as CuGeO 3 ͑Ref. 9͒ and KCuF 3 , 10 always have some weak interchain couplings present, which can change the physics at lowest energy and/or temperature. For example, strictly one-dimensional ͑1D͒ models do not exhibit phase transitions into states with broken symmetry, while real spin chain systems often develop Néel order at very low temperatures due to the weak ͑3D͒ interchain couplings. It is thus important to study the effects of these interchain couplings to fully understand the low-energy and/or temperature physics of real spin chain compounds.In this paper we study the low-energy collective excitations and dynamical response functions of weakly coupled, disordered AF spin-1 / 2 chains. Our work is motivated in part by the experimental studies on doped CuGeO 3 . In the absence of doping, it is a spin-Peierls system in which the spins dimerize and form a gapped, nonmagnetic ground state. Upon doping, the system becomes disordered, and both dimerization and spin gap get suppressed. Amazingly, when doping reaches certain levels the spins become Néel ordered at low temperature, which has been observed experimentally in Zn-and Si-doped CuGeO 3 . [11][12][13][14][15][16][17][18][19][20] Since these experimental discoveries a number of theoretical papers have addressed the static Néel ordering in these systems 24-36 using meanfield theory. On the other hand the collective excitations and dynamical response functions which have been studied experimentally using inelastic neutron scattering, 20 have not been studied theoretically thus far. The collective excitations and dynamical response functions are the subjects of the present work. We go beyond mean-field theory by allowing the Néel order parameter to fluctuate, and treat the interchain coupling using the random-phase a...

show abstract

Low-temperature properties of the random Heisenberg antiferromagnetic chain

Cited by 506 publications

References 11 publications

Quantum Spin-Liquid Behavior in the Spin-1/2 Random-Bond Heisenberg Antiferromagnet on the Kagome Lattice

Quantum Spin-Liquid Behavior in the Spin-1/2 Random-Bond Heisenberg Antiferromagnet on the Kagome Lattice

Absence of dynamical crossover in the vortex creep near by the second peak effect in superconducting Hg-1201 single crystals

Dynamics of weakly coupled random antiferromagnetic quantum spin chains

Contact Info

Product

Resources

About