Sharif Digital Repository

We have studied the phase diagram of the one-dimensional S= 1 2 XXZ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We have applied the quantum renormalization group (QRG) approach to obtain stable fixed points and the scaling of coupling constants. The QRG prescription has to be implemented to the second order of interblock interactions to obtain a self-similar Hamiltonian after each step of the QRG. This model shows a rich phase diagram which includes quantum spin-fluid and dimer phases in addition to the classical Néel and ferromagnetic ones. We have found the border between different phases by tracing the scaling of coupling constants.... 

We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes... 

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence bond states proposed in the Affleck-Kennedy-Lieb- Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, with uniform or alternating patterns of spins, which are ground states of Hamiltonians with nearest and next-nearest-neighbor interactions, and the partially dimerized or AKLT/valence bond solid states, which are constructed from them by projection. The latter states are translation-invariant ground states... 

We investigate quantum phase transitions in ladders of spin- 1 2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such models. We also study the behavior of entanglement between different neighboring sites near the transition point and show that quantum phase transitions in these systems are accompanied by divergences in derivatives of entanglement. © 2007 The American Physical Society  

We show that networks of spin-1 particles connected in a special geometry and subject to Affleck-Kennedy-Lieb-Tasaki (AKLT) interaction are capable of perfectly transferring states of particles (qubits and qutrits) if we also allow a global control of the network in predetermined time intervals. The geometry can be one, two, and three dimensional. The strengths of the couplings have the same modulus, and only their signs differ on various bonds. Any particle which is routed in the network acquires relative phase shifts which can be corrected after it is extracted from the network. An advantage of this protocol is that one can route more than one particle through the network simultaneously.... 

We study an open quantum spin chain of arbitrary length with nearest neighbor XX interactions of strength g, immersed in an external constant magnetic field Δ along the z direction, whose end spins are weakly coupled to two heat baths at different temperatures. In the so-called global approach, namely, without neglecting interspin interactions, using standard weak-coupling limit techniques, we first derive the open chain master equation written in terms of fermionic mode operators. Then, we focus on the study of the dependence of the resulting open dynamics from the ratio rg/Δ. By increasing r, some of the chain Bohr transition frequencies become negative; when this occurs, both the... 

We present the zero temperature phase diagram of the bond alternating Ising chain in the presence of Dzyaloshinskii-Moriya interaction. An abrupt change in ground state fidelity is a signature of quantum phase transition. We obtain the renormalization of fidelity in terms of quantum renormalization group without the need to know the ground state. We calculate the fidelity susceptibility and its scaling behavior close to quantum critical point (QCP) to find the critical exponent which governs the divergence of correlation length. The model consists of a long range antiferromagnetic order with nonzero staggered magnetization which is separated from a helical ordered phase at QCP. Our results... 

In this paper, we study the generation of Bell states between distant vertices in a permanently coupled quantum spin network, interacting via invariant stratification graphs. To begin with we establish a class of upper bounds over the achievable entanglement between the reference site and various vertices. We observe that the maximum of these upper bounds is one e-bit. We conclude that the reference site can generate a Bell state with a vertex if the corresponding upper bound of the vertex is one e-bit. Thus for generation of a Bell state this upper bound must be saturated. Taking this into account, we obtain the characteristic constraint of the proper graphs. We introduce a special class of... 

We investigate the creation of optimal entanglement in axially symmetric networks. The proposed network is one in which the connections are organized using a group table - in other words, using group association schemes. We show that optimal entanglement can be provided on such networks by adjusting couplings and the initial state. We find that the optimal initial state is a simple locally excited state. Moreover we obtain an analytic formula for the entanglement achievable between vertex pairs located in the same or conjugate strata and calculate their relevant optimal couplings. For those pairs located in non-conjugate strata, two upper bounds are presented. These results are also checked... 

We investigate the multiple use of a ferromagnetic spin chain for quantum and classical communications without resetting. We find that the memory of the state transmitted during the first use makes the spin chain a qualitatively different quantum channel during the second transmission, for which we find the relevant Kraus operators. We propose a parameter to quantify the amount of memory in the channel and find that it influences the quality of the channel, as reflected through fidelity and entanglement transmissible during the second use. For certain evolution times, the memory allows the channel to exceed the memoryless classical capacity (achieved by separable inputs) and in some cases it... 

We generalize an already proposed protocol for quantum state transfer to spin chains of arbitrary spin. An arbitrary unknown d -level state is transferred through a chain with rather good fidelity by the natural dynamics of the chain. We compare the performance of this protocol for various values of d. A by-product of our study is a much simpler method for picking up the state at the destination as compared with the one proposed previously. We also discuss entanglement distribution through such chains and show that the quality of entanglement transition increases with the number of levels d. © 2007 The American Physical Society  

We find exact solutions for a universal set of quantum gates on a scalable candidate for quantum computers, namely an array of two-level systems. The gates are constructed by a combination of dynamical and geometrical (non-Abelian) phases. Previously these gates have been constructed mostly on nonscalable systems and by numerical searches among the loops in the manifold of control parameters of the Hamiltonian. © 2005 The American Physical Society  

We investigate the phase diagram of an anisotropic ferrimagnetic spin-(1/2, 1) in the presence of a non-commuting (transverse) magnetic field. We find a magnetization plateau for the isotropic case while there is no plateau for the anisotropic ferrimagnet. The magnetization plateau can appear only when the Hamiltonian has the U(1) symmetry in the presence of the magnetic field. The anisotropic model is driven by the magnetic field from the Néel phase for low fields to the spin-flop phase for intermediate fields and then to the paramagnetic phase for high fields. We find the quantum critical points and their dependence on the anisotropy of the aforementioned field-induced quantum phase... 

Within the standard weak-coupling limit, the reduced dynamics of open quantum spin chains with their two end spins coupled to two distinct heat baths at different temperatures are mainly derived using the so-called global and local approaches, in which, respectively, the spin self-interaction is and is not taken into account. In order to compare the differences between the two regimes, we concentrate on an open three-site XX spin chain, provide systematic techniques to address the global and local asymptotic states, and then compare the asymptotic spin-transport features by studying the spin flux through the middle site. Based on the analytical expressions of the stationary states in the two... 

We have numerically studied the thermodynamic properties of the spin 1 2 XXZ chain in the presence of a transverse (noncommuting) magnetic field. The thermal, field dependence of specific heat and correlation functions for chains up to 20 sites has been calculated. The area where the specific heat decays exponentially is considered as a measure of the energy gap. We have also obtained the exchange interaction between chains in a bulk material using the random phase approximation and derived the phase diagram of the three-dimensional material with this approximation. The behavior of the structure factor at different momenta verifies the antiferromagnetic long-range order in the y direction... 

We show that the ground state of the Heisenberg spin-1/2 chain in an external magnetic field, can be exactly expressed as a matrix product state, provided that the coupling constants are constrained to be on a specific two dimensional surface. This ground state has a very interesting property: all the pairs of spins are equally entangled with each other. In this last respect, the results are of interest for engineering long-range entanglement in experimentally realizable finite arrays of qubits, where the ground state will act as the initial state of a quantum computer. © 2007 The American Physical Society