Boundaries and Unphysical Fixed Points in Dynamical Quantum Phase Transitions

Abstract

We show that dynamic quantum phase transitions (DQPT) in many situations involve renormalization group (RG) fixed points which are unphysical in the context of thermal phase transitions. In such cases, boundary conditions are shown to become relevant to the extent of even completely suppressing the bulk transitions. We establish these by performing exact RG analysis of the quantum Ising model on scale-invariant lattices of different dimensions, and by analyzing the zeros of the Loschmidt amplitude. Further corroboration of boundaries affecting the bulk transition comes from the three-state quantum Potts chain, for which we also show that the DQPT corresponds to a pair of period-2 fixed points.Dynamical quantum phase transitions (DQPT), a recent discovery of phase transitions, often periodic, in large quantum systems during time evolution [1-3], have generated a lot of interest because here time itself acts as the parameter inducing the transitions. Also, to be at a transition point, only time needs to be chosen properly without any requirement of fine-tuning of system parameters, unlike thermal transitions [4]. The signature of DQPT is the nonanalytic behaviour of various quantities in time around critical times t c 's. These transitions have now been shown in many models, like the transverse-field Ising model (TFIM), spin chains, quantum Potts models, the Kitaev model, and many others[1, 2, 6-10], and also observed experimentally [11,12]. In spite of being a zerotemperature quantum phenomenon, DQPT is not determined by the quantum phase transitions of the system but rather seems related to the classical thermal criticalities of an associated system [10]. However, despite the use of many techniques so far, very few exact results are known on the scaling and universality in DQPT [10]. Moreover, the natures of the possible phases and the transitions remain to be properly classified, e. g., whether only equilibrium phases and transitions would suffice or there can be specialities of its own [10].A general approach for phase transitions is the renormalization group (RG) framework [5] in terms of lengthdependent effective parameters and their flows to the fixed points (FP), with the stable FPs determining the allowed phases, and the unstable ones (or separatrices) the phase transitions. In this paper, we adopt an exact RG scheme for TFIM and the three-state quantum Potts chain (3QPC). Our exact results establish that there are DQPTs involving FPs that are unphysical in traditional thermal transitions. Secondly, we show that, for those unphysical FPs, boundary conditions (BC) are relevant and can even lead to a suppression of the transitions completely, unlike thermal cases where BCs do not affect the bulk transitions. Another surprising result is the emergence of a pair of period-2 FPs, never seen in the thermal context, that controls the DQPT in 3QPC, in contrast to the zero-temperature FP [2] for the Ising DQPT case. In short, our exact results bring out several distinctive features of DQPT, not to be found in equil...

Aperiodic dynamical quantum phase transition in multi-band Bloch Hamiltonian and its origin

“…and others [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. Additionally, several experiments have directly observed DQPTs, including trapped ions simulations [73][74][75][76], 53-qubit quantum simulations [77], nuclear magnetic resonance quantum simulators [78], quantum walks of photons [79,80], and spinor condensate simulations [81].…”

Dynamical quantum phase transitions in Stark quantum spin chains

“…1 This has been explored in many studies for both non-integrable 6,27-29 and integrable 19,21,[30][31][32] models. Further theoretical support also pointed out that for quenches not belonging to this class, the so-called "accidental" DQPTs can still occur, requiring a fine-tuning of the Hamiltonian [33][34][35][36][37][38] .…”

Dynamical Topological Quantum Phase Transitions at Criticality

“…This corespondence was verified in several subsequent studies for both non-integrable [40][41][42][43][44][45] and integrable [46][47][48][49][50][51][52][53] models. Further studies, however, reveal that DQPT is not in a one-to-one correspondence to EQPT, [54][55][56][57][58][59][60] suggesting that DQPT can, in general, be rather seen as a critical phenomenon distinct from the physics of EQPT 18,58,61 .…”