### Quantum Many-Body Systems

Quantum many-body systems appear very naturally in several fields of Physics, like Condensed Matter, High Energy Physics, quantum information or quantum biology. During the last years we have been working in the development of theoretical tools in order to describe many-body quantum systems.

The main problem in describing the states of a set of particles is that the number of parameters increases exponentially with the number of particles and then it is important to identify subsets in state space that are well suited to describe a certain system and allow for an efficient description. One may try to devise new ways of representing many-particle states so that physical quantities can be efficiently calculated. In this direction the study of entanglement in many-body systems has led to a deeper understanding of quantum phase transitions and the performance of numerical algorithms such as the density matrix renormalization group (DMRG) with allows to reduce the exponential grows of the complexity of the quantum system . Understanding the structure of state space and particular states such as ground and thermal states is one of the major topics in the quantum information theoretical assessment of many-body systems.

We work on the development and implementation of DMRG–and its time-dependent version tDMRG–methods, and use them to address problems drawn from an extremely broad range of topics in physics, biology and chemistry. The breadth of our DMRG and t-DMRG work is strongly driven by our recent development of a DMRG/tDMRG method which accurately simulates the dynamics and ground states of a huge class of open quantum systems. With this tool we are currently investigating dissipation, decoherence and irreversibility in many-body systems and important theoretical models such as the spin-boson model.

### Quantum effects in biology

Biologists do not take a quantum physics course during their studies because so far they were able to make sense of biological phenomena without using the counterintuitive quantum laws of physics that govern the atomic scale. However, in recent years progress in experimental technology has revealed that quantum phenomena are relevant for fundamental biological processes such as photosynthesis, magneto-reception and olfaction.

Photosynthesis is a fundamental biological process which provides the primary source of energy for almost all terrestrial life. In its early stages, ambient photons are absorbed by optically active molecules (pigments) in an antenna complex, leading to the formation of molecular excited states (excitons). These then migrate by excitation energy transfer (EET) through pigment–protein complexes (PPCs) to a reaction centre where the exciton’s energy is used to release an electron. Remarkably, these processes often have a quantum efficiency of almost 100%, and uncovering the underlying biological design principles could inspire important new developments in artificial light-harvesting technologies. The potential novelty of a biomimetic approach to light-harvesting is underlined by the unexpected observation of robust, long-lasting oscillatory features in two-dimensional spectra of PPCs extracted from bacteria, algae and higher plants.Using ultrafast non linear spectroscopy, sustained beating between optically excited states lasting several hundreds of femtoseconds at room temperature, and up to nearly 2ps in the Fenna–Matthews–Olson (FMO) complex at 77K, have been observed. These experiments have been interpreted as evidence for electronic coherences between excitons, with lifetimes which are, surprisingly, over an order of magnitude larger than coherences between electronic ground and excited states. Such coherence times are long enough for EET and excitonic coherence to coexist, conditions under which a sophisticated interplay of quantum and dissipative processes theoretically optimizes transport efficiency. Although many proposals for how quantum effects might enhance biological light-harvesting have been advanced over the past five years, most of these have used simple, phenomenological methods to include decoherence.

Environment assisted biological quantum dynamics: It is remarkable that quantum phenomena can play a role in warm, wet and noisy biological systems. One important reason is that some biologically relevant phenomena take place on rather short timescales that prevent the environment from destroying quantum coherence completely. We have proposed that environmental noise can actually collaborate with quantum dynamics to achieve the best possible efficiency in biological processes. We continue to explore this phenomenon with the aim of uncovering the design principles by which nature has optimized quantum biological function in noisy environments.

Environment assisted biological quantum dynamics: Biological environments are not merely creating white noise but do actually possess a complex spectral structure. Indeed, an important aspect of biological environments are vibrations which originate from proteins and embedded molecules. At specific frequencies this vibrational motion can be long-lived and interact in highly non-trivial fashion with electronic motion which we proposed to give rise to fast transport, molecular recognition or long-lived quantum coherence in biological systems.

Environment assisted biological quantum dynamics: Theory in this field needs to be verified by experiment. Indeed, recent advances in nonlinear optical spectroscopy have demonstrated the presence of long-lived quantum coherences in biological systems. These coherences reflect coherent features in biological processes, such as coherent transport and coherent electronic-vibrational (vibronic) coupling. Identification of the microscopic origin of experimentally observed coherences is a key to understanding the role of quantum effects in biological processes.

### Tensor network theory

A major research theme in our group is understands the nature of entanglement, correlations and quantum mutual information in ground states and thermal states of commonly encountered many-body systems. This has mainly involved exploiting and further developing sophisticated tensor network theory (TNT) techniques for efficiently simulating many-body quantum systems.

Currently this most prominently includes the density matrix renormalization group (DMRG) method and its generalization to time-dependent phenomena via the time-evolving block decimation (TEBD) algorithm applicable to one-dimensional systems. We are working in the extension of these methods to two-dimensional quantum lattice systems.

### Quantum Thermodinamics

The development of classical thermodynamics in the 19th century underpinned the Industrial Revolution, and the enormous economic growth and social changes that followed. Now, in the 21st century, the burgeoning quantum technological revolution promises unprecedented advances in our computation and communication capabilities, enabled by harnessing quantum coherence. As our

machines are scaled down into the quantum regime, it is of prime importance to understand how quantum mechanics affects the operation of these devices. This problem has attracted great interest to the field of quantum thermodynamics over the last few years.