Twist Method for Quantum Ground-State Problems and its Application to Antiferromagnetic Heisenberg Chains with Competing Interactions

Application of the interface approach in quantum Ising models

“…The scaling functions for ∆E c and ∆m are, however, similar. Apparently the scaling function g(x) for L∆E has the following form g(x) ∼ −x for x < 0 = 0 for x > 0 such that L∆E ∼ (Γ c − Γ)L which is the expected behaviour mentioned in [4].…”

“…The Ising chain in a transverse field is described by the Hamiltonian (4) and the ferromagnetic to paramagnetic phase transition occurs at Γ/J = 1 for S z = ±1. We take the basis states to be diagonal in the representation of S z .…”

“…In [4], it was argued that one should look at the scaling behaviour of the quantity L∆E which is expected to have a stiffness exponent = 1 for the transverse Ising chain (the same as that of the 2-d classical model). However, this is the same as saying ∆E scales as L 0 , and we do not find this behaviour (except, of course, at Γ = 0, but we are interested in the scaling behaviour near the critical point).…”

“…We apply the method of interfaces [2] in the Ising model and the anisotropic next nearest neighbour Ising (ANNNI) model [3] in a transverse field at zero temperature to study the quantum fluctuation driven transitions. In the process, we also explore the scope of the so called twist method [2,4] which we have shown to have additional features apart from the ones already known.…”

“…Recently, it has been shown in a variety of spin systems how the interfaces caused by twisting a system is closely linked to the phase transition. Apart from the application of the twist method to several classical models like Ising spins systems, Potts model and spin glasses [2], very recently it has been used for quantum ground state problems also [4]. In this method, the interface free energy is generated by the excess free energy between systems with and without a twist.…”