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Physical review. B, Condensed matter

Low-temperature specific heat of a random Heisenberg chain in the large- S limit

Ibrahim Avgin, David L. Huber

Published Aug 1, 1997• 5 citations
Publisher

Abstract

Results are presented for the low-temperature specific heat of a disordered Heisenberg chain with random $\ifmmode\pm\else\textpm\fi{}J$ interactions in the large-spin limit. The specific heat varies at ${T}^{2/3}$ with a coefficient that depends on the relative fractions of positive and negative bonds. The coefficient is calculated exactly for the equal-probability distribution. There is also a brief analysis of the destabilizing effects of an applied magnetic field.

DOI
10.1103/physrevb.56.2320

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Results are presented for the low-temperature specific heat of a disordered Heisenberg chain with random \ifmmode±\else\textpm\fiJ\ifmmode\pm\else\textpm\fi{}J\ifmmode±\else\textpm\fiJ interactions in the large-spin limit. The specific heat varies at T2/3{T}^{2/3}T2/3 with a coefficient that depends on the relative fractions of positive and negative bonds. The coefficient is calculated exactly for the equal-probability distribution. There is also a brief analysis of the destabilizing effects of an applied magnetic field.
The Heisenberg chain with random $\ifmmode\pm\else\textpm\fi{}J$ bonds is studied for the quantum spin s=12s=\frac{1}{2}s=21​ and in the classical limit. The former is treated by high-temperature expansion and transfer matrix calculation while the latter can be analyzed exactly. The disorder leads to a 1T\frac{1}{T}T1​ behavior of the low-temperature susceptibility in the classical system. For s=12s=\frac{1}{2}s=21​ our analysis reveals a significant residual entropy at low temperature. From this we conclude that for quantum spins the susceptibility exhibits three different regimes in temperature and that the specific heat has a peak in the very low-temperature regime.
The one-dimensional quantum Heisenberg model with random \ifmmode\pm\else\textpm\fi{}J bonds is studied for S=1/2 and S=1. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and the quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite-size systems.
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.
The low-temperature thermodynamic properties of a random antiferromagnetic Heisenberg chain in zero magnetic field are studied approximately by a renormalisation group method. The couplings J obey a probability distribution function P(J) approximately 1/J alpha , with alpha a constant. It is found that the susceptibility chi and the specific heat C behave like chi approximately T - alpha chi and C approximately T 1- alpha c at low temperatures alpha chi and alpha c are weakly varying functions of temperature and slowly approach unity as T goes to zero. Comparison of these results with other theoretical analysis as well as experimental results on organic charge transfer compounds is also discussed.
Quenched disorders can strongly influence the physical properties of quantum many-body systems. The real-space strong-disorder renormalization group (SDRG) analysis has shown that the spin-1/2 random Heisenberg chain is controlled by the infinite-randomness fixed point (IRFP) and forms a random singlet (RS) ground state. Motivated by recent thermal transport experiments on the quasi-one-dimensional antiferromagnet copper benzoate [B. Y. Pan et al., Phys. Rev. Lett. 129, 167201 (2022)], we adapt the SDRG to study the low-temperature properties of the random Heisenberg chain by assuming that its low-energy excited states are captured by the parent Hamiltonian of the RS ground state as well. We find that while the specific heat coefficient and the uniform magnetic susceptibility scale as $C/T\ensuremath{\sim}{T}^{\ensuremath{-}{\ensuremath{\alpha}}_{c}}$ and $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}{\ensuremath{\alpha}}_{s}}$ with $0<{\ensuremath{\alpha}}_{c,s}<1$, indicating a divergent low-energy density of states, the thermal and the spin conductivities scale as $\ensuremath{\kappa}/T\ensuremath{\sim}T$ and ${\ensuremath{\sigma}}_{s}\ensuremath{\sim}T$, which implies a vanishing density of extended states in the low-energy limit. We believe that such a disparity in the thermodynamic and transport properties is a common feature of random systems controlled by the IRFP.
Low energy asymptotics of the behavior of static and dynamic susceptibility, specific heat, correlation length, Knight shift, etc. (which can be measured experimentally) of the integrable disordered quantum spin 12\frac{1}{2}21​ Heisenberg chain are calculated analytically. For some experimentally essential distributions of the strong disorder we show how the latter renormalizes the universal low-energy characteristics of the system and causes the low temperature divergencies.