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arXiv:cond-mat/0307266

Quantum phase transition in easy-axis antiferromagnetic integer-spin chains

Massimo Capone, S. Caprara, L. Cataldi

Published Jul 11, 2003• 1 citation
arXivHTMLPDF

Abstract

Antiferromagnetic Heisenberg integer-spin chains are characterized by a spin-liquid ground state with no long-range order, due to the relevance of quantum fluctuations. Spin anisotropy, however, freezes quantum fluctuations, and the system is magnetized in the presence of a sufficiently large easy-axis anisotropy. We numerically investigate the case S=1, by means of the density-matrix renormalization group, and find that the freezing of the spin liquid into a Néel spin solid, with increasing easy-axis anisotropy, is a continuous quantum phase transition. Numerical evidence indicates that the transition is not in the two-dimensional Ising universality class.

DOI
10.48550/arxiv.cond-mat/0307266

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Antiferromagnetic Heisenberg integer-spin chains are characterized by a spin-liquid ground state with no long-range order, due to the relevance of quantum fluctuations. Spin anisotropy, however, freezes quantum fluctuations, and the system is magnetized in the presence of a sufficiently large easy-axis anisotropy. We numerically investigate the case S=1, by means of the density-matrix renormalization group, and find that the freezing of the spin liquid into a Néel spin solid, with increasing easy-axis anisotropy, is a continuous quantum phase transition. Numerical evidence indicates that the transition is not in the two-dimensional Ising universality class.
The fidelity and entropy in an easy-axis antiferromagnetic Heisenberg spin-1 chain are studied numerically. By using the method of density-matrix renormalization group, the effects of anisotropy on fidelity and entanglement entropy are investigated. Their relations with quantum phase transition are analyzed. It is found that the quantum phase transition from the Haldane spin liquid to N\'eel spin solid can be well characterized by the fidelity. The phase transition can be hardly detected by the entropy but it can be successfully detected by the first deviation of the entropy.
The ground-state phase diagram of S=2S=2S=2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-DDD, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a generalization of that introduced by Dasgupta and Ma. Random-singlet phases occur in which each spin is paired with one other spin that may be very far away; more exotic phases also occur. The behavior of typical and mean correlation functions is analyzed and found to be very different, with very small sets of spins dominating the latter at long distances as well as the low-temperature thermodynamics. Some of the phase transitions that occur between antiferromagnetically ordered phases and random singlet or other antiferromagnetic phases are also analyzed. For example, if a small uniaxial anisotropy perturbation is added to a random Heisenberg antiferromagnetic chain, a transition occurs from a random-singlet phase to an Ising antiferromagnetic phase, as the anisotropy changes sign from easy plane to easy axis. The staggered magnetization vanishes at the transition with critical exponent \ensuremath{\beta}=8/(1+ \ensuremath{\surd}7 ). Possible implications for the properties of random quantum magnetic systems in higher dimensions are briefly discussed.
Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic S=1S=1S=1 Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid phases as well as the spin-liquid and ferromagnetic phases. Analyzing spin-correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.
We study the S =1 antiferromagnetic Heisenberg chain with the anisotropies E ∑ j [( S j x ) 2 -( S j y ) 2 ] and D ∑ j ( S j x ) 2 in a magnetic field H along z -axis, using numerical diagonalization up to N =14 and the finite-size scaling and phenomenological renormalization. We give the phase diagrams in the H E and H D planes repectively at T =0. It is found that a magnetic field breaking the axial symmetry of the Hamiltonian brings about canted Néel order for H c1 < H < H c2 , if the system has the Haldane gap. The two transitions at H c1 and H c2 are revealed to belong to the same universality class as the two-dimensional Ising model. In addition it is found that even if the system is in the large- D phase ( D > D c ≈1), the same transitions occur in the region where the value of D is about 1.0∼1.5.
When quantum effects are small, Heisenberg antiferromagnets have a Néel ordered ground state, but strong zero-point fluctuations can lead to new ‘‘exotic’’ spin-liquid ground states without long-range Néel order. These effects are strongest in low dimensions and frustrated systems, and always occur in one dimension. The nature of the new ground state can depend on whether the microscopic spins have integer or half-integer S. As an example of such systems the rich phase diagram of the one-dimensional S=1 Heisenberg antiferromagnet with additional biquadratic exchange and uniaxial on-site anisotropy will be discussed in detail.