Localization and topology protected quantum coherence at the edge of hot matter

Abstract

Topological phases are characterized by edge states confined near the boundaries by a bulk energy gap. On raising temperature, these edge states are typically lost due to mobile thermal excitations. However, disorder can localize an isolated many-body system, potentially allowing for a sharply defined topological phase even in a highly excited state. We explicitly demonstrate this in a model of a disordered, one-dimensional magnet with spin one-half edge excitations. Furthermore, we show that the time evolution of a simple, highly excited state reveals quantum coherent edge spins. In particular, we demonstrate the coherent revival of an edge spin over a time scale that grows exponentially with system size. This is in sharp contrast to the general expectation that quantum bits strongly coupled with a hot many-body system will rapidly lose coherence. This result opens new directions in the study of topologically protected quantum dynamics.

Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems

“…While the first is ameliorated via MBL (Fig. 2a), the second is intrinsic to the stroboscopic approach-the ESPT phase is stable only up to a finite parametric time scale, T * 2,symm ∼ (h 2 /ω) −1 , beyond which the protecting symmetry is broken.The first effect is reminiscent of similar discussions in the static context [19][20][21], where disorder can localize thermal bulk excitations and suppress scattering. Since the edge operators are odd under the Z 2 × Z 2 symmetry, their dressed MBL counterparts will not appear in the effective "l-bit" Hamiltonian [60,61] and dephasing occurs solely via coupling to the other edge mode [21] on a time scale that is exponential in system size, T * 2,MBL ∼ e O(N ) [78], as depicted in Fig.…”

“…This difficulty is further exacerbated for isolated atomic systems, where the lack of coupling to an external bath renders the system incapable of releasing excess energy and entropy [58]. A fruitful strategy for combating such heating is to harness many-body localization (MBL) [23,[59][60][61][62], which has been predicted to stabilize quantum coherent behavior without the need for stringent cooling or adiabatic preparation of low temperature many-body states [19][20][21]63].…”

“…In principle, cold-atom quantum simulations could offer a powerful additional tool set-including locally-resolved measurements and interferometric protocols-for probing the robustness of edge modes and systematically exploring their stability to specific perturbations [14][15][16][17][18]. Moreover, such platforms could also enable the controlled storage and transmission of quantum information [19][20][21]. Despite these advantages, and owing to the complexity of typical model SPT Hamiltonians, it remains difficult to engineer and stabilize SPT phases in coldatom systems.…”

Low-frequency conductivity in many-body localized systems

“…Instead, an isolated system in the MBL phase is a "quantum memory", retaining some local memory of its local initial conditions at arbitrarily late times [9][10][11][12][13][14][15][16][17][18]. The existence of the MBL phase can be proved with minimal assumptions [20]; many of its properties are phenomenologically understood [10,11,16], and some cases can be explored using strong-randomness renormalization group methods [9,[21][22][23].…”

Scaling Theory of Entanglement at the Many-Body Localization Transition

“…In such many-body localized (MBL) systems [18][19][20], generic eigenstates have properties akin to those of ground states. They exhibit short-range entanglement that scales like the perimeter of the subregion [17] ("area law"), and have quantum coherent dynamics up to arbitrarily long time scales [21][22][23][24][25][26][27], even at high energy densities [17,26,[28][29][30][31].…”