First order quantum phase transitions of the XX spin-1/2 chain in a uniform transverse field

Exact diagonalization for spin-1/2 chains and the first order quantum phase transitions of the XXX chain in a uniform transverse field

“…(t) when the control parameter t changes from 1 to 0 similar to the situation of XX spin-1 2 chain reported in [17]. Obviously, the quantum phase transitions occurring in such cases are of the first order.…”

“…Obviously, the quantum phase transitions occurring in such cases are of the first order. [17] It can be verified by the code that all levels with eigenenergy E k min (t) for k = 1, 2, • • • , [N/2] are not degenerate for N even and 0 ≤ t ≤ 1, while they are all two-fold degenerate for N odd and 0 < t < 1. The degeneracy of the ground state for N odd at t = 0 is 2(2S + 1) = 4, while the ground state for N odd at t = 1 is a singlet with S = N/2 and S 0 = −N/2.…”

Effect of Substrate Temperature on Epitaxial Orientation of Rh Thin Films Sputtered on A-Plane Sapphire

“…Though only a 10-qubit system was considered in [28], the level-crossings related to the ground state of the system are quite similar to the results reported in the present work. Though the level patterns and the level-crossing positions are different from those of the XX spin-1/2 chain studied previously in [17] and the LMG model in [30], the quantum phase transition behavior in all these systems is similar, and should be common to other spin interaction systems in a uniform transverse field.…”

“…We have verified that the ground state energy of the system is related to the following set of eigenenergies: (t) when the control parameter t changes from 1 to 0 similar to the situation of the XX spin-1 2 chain reported in [17]. Obviously, the quantum phase transitions occurring in such cases are of first order [17]. It can be verified by the code that all levels with eigenenergy E k min (t) for k = 1, 2, .…”

“…The simple code can easily be used to study general one-dimensional spin-1/2 interaction systems, such as XY or XYZ spin-1/2 chains. As an example, the code is applied to study XXX spin-1/2 chains with nearest neighbor interaction in a uniform transverse field, showing that there are a series of level-crossing points when the interaction strength and magnitude of the magnetic field satisfy certain conditions similar to the situation in the XX spin chain studied in [17]. The entanglement measure [18,19] defined in terms of the von Neumann entropy of one-body reduced density matrix is used to measure the multi-particle entanglement and reveal the QPTs in the system.…”