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Register a new userDMRG Study of Critical Behavior of the Spin-1/2 Alternating Heisenberg Chain
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We investigate the critical behavior of the S=1/2 alternating Heisenberg chain using the density matrix renormalization group (DMRG). The ground-state energy per spin and singlet-triplet energy gap are determined for a range of alternations. Our results for the approach of the ground-state energy to the uniform chain limit are well described by a power law with exponent p=1.45. The singlet-triplet gap is also well described by a power law, with a critical exponent of p=0.73, half of the ground-state energy exponent. The renormalization group predictions of power laws with logarithmic corrections can also accurately describe our data provided that a surprisingly large scale parameter is present in the logarithm.
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We investigate the critical relaxational dynamics of the S=1/2 Heisenberg ferromagnet on a simple cubic lattice within the Handscomb prescription on which it is a diagrammatic series expansion of the partition function that is computed by means of a Monte Carlo procedure. Using a phenomenological renormalization group analysis of graph quantities related to the spin susceptibility and order parameter, we obtain precise estimates for the critical exponents relations $gamma / u = 1.98pm 0.01 $ and $beta / u = 0.512 pm 0.002$ and for the Curie temperature $k_BT_c/J = 1.6778 pm 0.0002$. The critical correlation time of both energy and susceptibility is also computed. We found that the number of Monte Carlo steps needed to generate uncorrelated diagram configurations scales with the systems volume. We estimate the efficiency of the Handscomb method comparing its ability in dealing with the critical slowing down with that of other quantum and classical Monte Carlo prescriptions.
A few paradigmatic one-dimensional lattice-statistical spin models have recently attracted a vigorous scientific interest owing to their peculiar thermodynamic behavior, which is highly reminiscent of a temperature-driven phase transition. The pseudotransitions of one-dimensional lattice-statistical spin models differ from actual phase transitions in several important aspects: the first-order derivatives of the Gibbs free energy such as entropy or magnetization exhibit near a pseudo-transition an abrupt continuous change instead of a true discontinuity, whereas the second-order derivatives of the Gibbs free energy such as specific heat or susceptibility display near a pseudo-transition a vigorous finite peak instead of an actual power-law divergence. In the present chapter we will comprehensively examine a pseudo-critical behavior of the spin-1/2 Ising diamond and tetrahedral chains by a detailed examination of basic magnetothermodynamic quantities such as the entropy, specific heat and susceptibility. It will be demonstrated that density plots of these magnetothermodynamic quantities provide a useful tool for establishing a finite-temperature diagram, which clearly delimits boundaries between individual quasi-phases in spite of a lack of true spontaneous long-range order at any nonzero temperature. It is suggested that a substantial difference between the degeneracies of two ground states of the spin-1/2 Ising diamond and tetrahedral chains is an essential prerequisite for observation of a relevant pseudo-critical behavior in a close vicinity of their ground-state phase boundary.
By using the infinite time-evolving block decimation, we study quantum fidelity and entanglement entropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field. The effects of the magnetic field on the fidelity are investigated, and its relation with the quantum phase transition (QPT) is analyzed. The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase. The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge c = 1 is obtained. We also study the relationship between the quantum coherence, string order parameter and QPTs. Results obtained from these quantum information observations are consistent with the previous reports.
In conformal field theory, key properties of spin-1/2 chains, such as the ground state energy per site and the excitation gap scale with dimerization delta as delta^alpha with known exponents alpha and logarithmic corrections. The logarithmic corrections vanish in a spin chain with nearest (J=1) and next nearest neighbor interactions (J_2), for J_2c=0.2411. DMRG analysis of a frustrated spin chain with no logarithmic corrections yields the field theoretic values of alpha, and the scaling relation is valid up to the physically realized range, delta ~ 0.1. However, chains with logarithmic corrections (J_2<0.2411 J) are more accurately fit by simple power laws with different exponents for physically realized dimerizations. We show the exponents decreasing from approximately 3/4 to 2/3 for the spin gap and from approximately 3/2 to 4/3 for the energy per site and error bars in the exponent also decrease as J_2 approaches to J_2c.
We have measured the specific heat of an S=1/2 antiferromagnetic alternating Heisenberg chain pentafulorophenyl nitronyl nitroxide under magnetic fields up to H>H_C2. This compound has the field-induced magnetic ordered (FIMO) phase between H_C1 and H_C2. Characteristic behaviors are observed depending on the magnetic field up to above H_C2 outside of the H-T boundary for the FIMO. Temperature and field dependence of the specific heat are qualitatively in good agreement with the theoretical calculation on an S=1/2 two-leg ladder. [Wang et al. Phys. Rev. Lett 84 5399 (2000)] This agreement suggests that the observed behaviors are related with the low-energy excitation in the Tomonaga-Luttinger liquid.
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