arXiv subjects

Shaon Sahoo

Publications and source records attributed to Shaon Sahoo.

27 records · Page 2Linked to original sources

arXiv2014

Studies on a frustrated Heisenberg spin chain with alternating ferromagnetic and antiferromagnetic exchanges

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is present due to the non-zero $J_2^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. For fixed $J_1^F$, the phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

cond-mat.str-el↗

arXiv2014

Optimal linear Kawasaki model

The Kawasaki model is not exactly solvable as any choice of the exchange rate ($w_{jj'}$) which satisfies the detailed balance condition is highly nonlinear. In this work we address the issue of writing $w_{jj'}$ in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. In the continuum limit, our approach leads to a Cahn-Hilliard equation of conservative dynamics. The work presented in this paper will help us anticipate how the conservative dynamics of an arbitrary Ising system depends on the temperature and the coupling constants. In particular, for two and three dimensional systems, the critical temperatures estimated in our work are in good agreement with the actual values. We also calculate the dynamic and some of the critical exponents of the model.

cond-mat.stat-mech↗

arXiv2013

Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction $J_2$) and dimerization ($δ$). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the $J_2-δ$ plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

cond-mat.str-el↗

arXiv2012

Entanglement Localization and Optimal Measurement

The entanglement can be localized between two noncomplementary parts of a many-body system by performing measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). We derive here a generic optimality condition for the LE, which, besides being helpful in studying tripartite systems in pure states, can also be of use in studying mixed states of general bipartite systems. We further discuss a canonical way of localizing entanglement, where the BSM is not chosen arbitrarily, but is fully determined by the properties of the system. The LE obtained in this way, we call the localized entanglement by canonical measurement (LECM), is not only operationally meaningful and easy to calculate in practice (without needing any demanding optimization procedure), it provides a nice way to define the entanglement length in many-body systems. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end, some numerical results are presented for $j_1-j_2$ spin model to demonstrate how the LECM behaves.

quant-ph↗

arXiv2012

Study of Low Temperature Magnetic Properties of a Single Chain Magnet With Alternate Isotropic and Non-Collinear Anisotropic Units

Here we study thermodynamic properties of an important class of single-chain magnets (SCMs), where alternate units are isotropic and anisotropic with anisotropy axes being non-collinear. This class of SCMs shows slow relaxation at low temperatures which results from the interplay of two different relaxation mechanisms, namely dynamical and thermal. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. We here show how statistical behavior of this class of SCMs can be studied using a transfer matrix (TM) method. We also, for the first time, discuss in detail how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. At the end of this paper, we apply this technique to study a real helical chain magnet.

cond-mat.stat-mech↗

arXiv2011

Exact Entanglement Studies of Strongly Correlated Systems: Role of Long-Range Interactions and Symmetries of the System

We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.

quant-ph↗

arXiv2011

Full Spin and Spatial Symmetry Adapted Technique for Correlated Electronic Hamiltonians: Application to an Icosahedral Cluster

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non-Abelian point group. Here we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z-component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non-Abelian point group. The $C_{60}$ molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach.

physics.atm-clus↗

arXiv2010

Inverse Vector Operators

In different branches of physics, we frequently deal with vector del operator ($\vec{\nabla}$). This del operator is generally used to find curl or divergence of a vector function or gradient of a scalar function. In many important cases, we need to know the parent vector whose curl or divergence is known or require to find the parent scalar function whose gradient is known. But the task is not very easy, especially in case of finding vector potential whose curl is known. Here,'inverse curl', 'inverse divergence' and 'inverse gradient' operators are defined to solve those problems easily. All operators are defined in the orthogonal curvilinear co-ordinate system.

math-ph↗

arXiv2008

Fully Symmetrized VB Based Technique for Solving Exchange Hamiltonians of Molecular Magnets

Generally, the first step in modeling molecular magnets involves obtaining the low-lying eigenstates of a Heisenberg exchange Hamiltonian which conserves total spin and belongs usually to a non-Abelian point group. In quantum chemistry, it has been a long standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of the point group. Many attempts have been made over years, but unfortunately these have not resulted in methods that are easy to implement, or even applicable to all point groups. Here we present a general technique which is a hybrid method based on VB basis and constant Ms basis, which is applicable to all types of point groups, easy to implement on computer. We illustrate the power of the method by applying it to the molecular magnetic system, Cu6Fe8, with cubic symmetry. We emphasize that our method is applicable to spin clusters with arbitrary site spins and is easily extended to Fermionic systems.

physics.chem-ph↗