We construct a model Hamiltonian for $S=2$ spin chain, where a variable parameter $\ensuremath{\alpha}$ is introduced. The edge spin is $S=1$ for $\ensuremath{\alpha}=0$ and $S=3/2$ for $\ensuremath{\alpha}=1$. Due to the topological distinction of the edge states, these two phases must be separated by one or several topological quantum phase transitions. We have studied the quantum phase transition by density matrix renormalization group calculation and proposed a phase diagram for this model.We construct a model Hamiltonian for $S=2$ spin chain, where a variable parameter $\ensuremath{\alpha}$ is introduced. The edge spin is $S=1$ for $\ensuremath{\alpha}=0$ and $S=3/2$ for $\ensuremath{\alpha}=1$. Due to the topological distinction of the edge states, these two phases must be separated by one or several topological quantum phase transitions. We have studied the quantum phase transition by density matrix renormalization group calculation and proposed a phase diagram for this model.

arXiv:1002.0966Physical Review BJun 24, 201021 citations

Dynamical topological quantum phase transitions in a finite-size spin system

Shaoying Yin, Hongchun Sun, Jin‐Liang Guo +2 more

Chinese Journal of PhysicsNov 21, 20251 citation

PHASE TRANSITIONS IN QUANTUM SPIN CHAINS

Jenő Sólyom

WORLD SCIENTIFIC eBooksApr 1, 19920 citations

Discriminating string order parameter for topological phases of gapped SU(N) spin chains

Kasper Duivenvoorden, Thomas Quella

One-dimensional gapped spin chains with symmetry $PSU(N)=SU(N)/{\mathbb{Z}}_{N}$ are known to possess $N$ different topological phases. In this paper, we introduce a nonlocal string order parameter which characterizes each of these $N$ phases unambiguously. Numerics confirm that our order parameter allows one to extract a quantized topological invariant from a given nondegenerate gapped ground state wave function. Discontinuous jumps in the discrete topological order that arise when varying physical couplings in the Hamiltonian may be used to detect quantum phase transitions between different topological phases.One-dimensional gapped spin chains with symmetry $PSU(N)=SU(N)/{\mathbb{Z}}_{N}$ are known to possess $N$ different topological phases. In this paper, we introduce a nonlocal string order parameter which characterizes each of these $N$ phases unambiguously. Numerics confirm that our order parameter allows one to extract a quantized topological invariant from a given nondegenerate gapped ground state wave function. Discontinuous jumps in the discrete topological order that arise when varying physical couplings in the Hamiltonian may be used to detect quantum phase transitions between different topological phases.

arXiv:1208.0697Physical Review BDec 26, 201230 citations

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

Jing-Min Zhu

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -spin maximal entanglement.We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -spin maximal entanglement.

Chinese Physics COct 1, 20141 citation

First-order topological quantum phase transitions in strongly correlated one-dimensional systems

Simone Barbarino

Bulletin of the American Physical SocietyMar 6, 20190 citations

We construct a model Hamiltonian for

S=2

spin chain, where a variable parameter $\ensuremath{\alpha}$ is introduced. The edge spin is

S=1

for $\ensuremath{\alpha}=0$ and

S=3/2

for $\ensuremath{\alpha}=1$. Due to the topological distinction of the edge states, these two phases must be separated by one or several topological quantum phase transitions. We have studied the quantum phase transition by density matrix renormalization group calculation and proposed a phase diagram for this model.

One-dimensional gapped spin chains with symmetry

PSU(N)=SU(N)/{\mathbb{Z}}_{N}

are known to possess

N

different topological phases. In this paper, we introduce a nonlocal string order parameter which characterizes each of these

N

phases unambiguously. Numerics confirm that our order parameter allows one to extract a quantized topological invariant from a given nondegenerate gapped ground state wave function. Discontinuous jumps in the discrete topological order that arise when varying physical couplings in the Hamiltonian may be used to detect quantum phase transitions between different topological phases.